DOI QR코드

DOI QR Code

Thickness of shear flow path in RC beams at maximum torsional strength

  • Kim, Hyeong-Gook (Department of Architectural and Urban System Engineering, Kongju National University) ;
  • Lee, Jung-Yoon (School of Civil and Architectural Engineering, Sungkyunkwan University) ;
  • Kim, Kil-Hee (Department of Architectural and Urban System Engineering, Kongju National University)
  • 투고 : 2022.01.10
  • 심사 : 2022.04.28
  • 발행 : 2022.05.25

초록

The current design equations for predicting the torsional capacity of RC members underestimate the torsional strength of under-reinforced members and overestimate the torsional strength of over-reinforced members. This is because the design equations consider only the yield strength of torsional reinforcement and the cross-sectional properties of members in determining the torsional capacity. This paper presents an analytical model to predict the thickness of shear flow path in RC beams subjected to pure torsion. The analytical model assumes that torsional reinforcement resists torsional moment with a sufficient deformation capacity until concrete fails by crushing. The ACI 318 code is modified by applying analytical results from the proposed model such as the average stress of torsional reinforcement and the effective gross area enclosed by the shear flow path. Comparison of the calculated and observed torsional strengths of existing 129 test beams showed good agreement. Two design variables related to the compressive strength of concrete in the proposed model are approximated for design application. The accuracy of the ACI 318 code for the over-reinforced test beams improved somewhat with the use of the approximations for the average stresses of reinforcements and the effective gross area enclosed by the shear flow path.

키워드

과제정보

This work was supported by the Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2019R1A6A1A03032988); This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2018R1A2B3001656); This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2019R1I1A3A01058156); This research was supported by UNDERGROUND CITY OF THE FUTURE program funded by the Ministry of Science and ICT.

참고문헌

  1. ACI Committee (2019), Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary, American Concrete Institute, Farmington Hills, USA.
  2. Adebar, P. (1989), "Shear design of concrete offshore structures", Ph.D. Dissertation of Philosophy, University of Toronto, Toronto.
  3. Belarbi, A. and Hsu, T.T.C. (1994), "Constitutive laws of concrete in tension and reinforcing bars stiffened by concrete", ACI Struct. J., 91(4), 465-474.
  4. Bernardo, L.F.A. (2019), "Generalized softened variable angle truss model", Mater., 12(13), 1-24. https://doi.org/10.1186/s40069-018-0285-0.
  5. Bernardo, L.F.A. and Lopes, S.M.R. (2009), "Torsion in HSC hollow beams: strength and ductility analysis", ACI Struct. J., 106(1), 39-48.
  6. Bernardo, L.F.A., Andrade, J.M.A. and Lopes, S.M.R. (2012), "Softened truss model for reinforced NSC and HSC beams under torsion: A comparative study", Eng. Struct., 42, 278-296. https://doi.org/10.1016/j.engstruct.2012.04.036.
  7. Chen, S. and Kabeyasawa, T. (2004), "Average stress-strain relationship of steel bars embedded in concrete", Proceeding of the 13th World Conference on Earthquake Engineering, Vancouver, August.
  8. Choi, J.K. and Lee, S.C. (2019), "Sectional analysis procedure for reinforced concrete members subjected to pure torsion", Adv. Civ. Eng., 6019321. https://doi.org/10.1155/2019/6019321.
  9. Comite Euro-International du Beton (CEB) (1990), CEB-FIP model code 1990, Comite Euro-International du Beton (CEB), London, UK.
  10. CSA Committee A23.3:19 (2019), Design of Concrete Structures, Canadian Standards Association, Toronto, ON, Canada.
  11. EC2 (2005), Eurocode 2: Design of Concrete Structures-Part 1-1: General Rules and Rules for Buildings, European Committee for Standardization (CEN), Brussels, Belgium.
  12. El-Degwy, W.M. and McMullen, A.E. (1985), "Prestressed concrete tests compared with torsion theories", PCI J., 30(5), 96-127. https://doi.org/10.15554/pcij.09011985.96.127
  13. Fang, I.K. and Shiau, J.K. (2004), "Torsional behavior of normal-and high-strength concrete beams", ACI Struct. J., 101(3), 304-313.
  14. Hsu, T.T.C. (1968), "Torsion of structural concrete-Behavior of reinforced concrete rectangular members", Torsion of structural concrete, SP18, American Concrete Institute, Detroit, 261-306.
  15. Hsu, T.T.C. (1988), "Softened truss model theory for shear and torsion", ACI Struct. J., 85(6), 624-635.
  16. Hsu, T.T.C. (1990), "Shear flow zone in torsion of reinforced concrete", J. Struct. Eng. ASCE, 116(11), 3206-3226. https://doi.org/10.1061/(ASCE)0733-9445(1990)116:11(3206)
  17. Ibraheem, O.F. and Mukhlif, O.A. (2021), "Torsional behavior of reinforced concrete plates under pure torsion", Comput. Concrete, 28(3), 311-319. https://doi.org/10.12989/cac.2021.28.3.311.
  18. Jeong, Y.S., Kwon, M.H. and Kim, J.S. (2021), "Development of a lattice model for predicting nonlinear torsional behavior of RC beams", Struct. Eng. Mech., 79(6), 779-789. https://doi.org/10.12989/sem.2021.79.6.779.
  19. JSCE Guidelines for Concrete (2007), Standard Specifications for Concrete Structures, Japan Society of Civil Engineering, Tokyo, Japan.
  20. Ju, H.J., Han, S.J., Kim, K.S., Strauss, A. and Wu, W. (2020), "Multi-potential capacity for reinforced concrete members under pure torsion", Struct. Eng. Mech., 75(3), 401-414. https://doi.org/10.12989/sem.2020.75.3.401.
  21. Kanakubo, T. and Hosoya, H. (2015), "Bond splitting strength of reinforced strain-hardening cement composite elements with small bar spacing", ACI Struct. J., 112(17), 189-198.
  22. Kanakubo, T., Yonemaru, K. and Fukuyama, H. (1997), "Study on bond splitting behavior of reinforced concrete members: Part 1 - Local bond stress and slippage without lateral reinforcement", J. Struct. Constr. Eng., 492, 99-106.
  23. Kim, C., Kim, S., Kim, K.H., Shin, D., Haroon, M. and Lee, J.Y. (2019), "Torsional behavior of reinforced concrete beams with high-strength steel bars", ACI Struct. J., 116(6), 251-263.
  24. Kim, M.J., Kim, H.G., Lee, Y.J., Kim, D.H., Lee, J.Y. and Kim, K.H. (2020), "Pure torsional behavior of RC beams in relation to the amount of torsional reinforcement and cross-sectional properties", Const. Build. Mater., 260(10), 1-17. https://doi.org/10.1016/j.conbuildmat.2020.119801.
  25. Kim, S.W., Kim, Y.S., Kim, M.J., Lee, J.S. and Kim, K.H. (2014), "Evaluation of bond performance of RC beams with U-shaped reinforcement", Struct. Eng. Int., 124(3), 330-340. https://doi.org/10.2749/101686614X13830788506440.
  26. Kuan, A., Bruun, E.P.G, Bentz, E.C. and Collins, M.P. (2019), "Nonlinear sectional analysis of reinforced concrete beams and shells subjected to pure torsion", Comput. Struct., 222, 118-132. https://doi.org/10.1016/j.compstruc.2019.07.001.
  27. Lee, J.Y. and Kim, S.W. (2010), "Torsional strength of RC beams considering tension stiffening effect", J. Struct. Eng., 136(11), 1367-1378. https://doi.org/10.1061/(asce)st.1943-541x.0000237
  28. Lee, J.Y. and Kim, U.Y (2008), "Effect of longitudinal tensile reinforcement ratio and shear span-to-depth ratio on minimum shear reinforcement in beams", ACI Struct. J., 105(2), 134-144.
  29. Lee, J.Y., Kim, K.H., Lee, S.H., Kim, C.H. and Kim, M.H. (2018), "Maximum torsional reinforcement of reinforced concrete beams subjected to pure torsion", ACI Struct. J., 115(3), 749-760.
  30. Maekawa, K., Pimanmas, A. and Okamura, H. (2003), Nonlinear Mechanics of Reinforced Concrete, CRC Press.
  31. McMullen, A.E. and Rangan, V. (1978). "Pure torsion in rectangular sections-A re-examination", ACI Struct. J. Proc., 75(10), 511-519.
  32. Mitchell, D. and Collins, M.P. (1974), "Behavior of structural concrete beams in pure torsion", Department of Civil Engineering, University of Toronto, Publication No. 74-06, 88.
  33. Peng, X.N. and Wong, Y.L. (2011), "Behavior of reinforced concrete walls subjected to monotonic pure torsion-An experimental study", Eng. Struct., 33, 4295-2508. https://doi.org/10.1016/j.engstruct.2011.04.022.
  34. Rahal, K.N. (2021), "A unified approach to shear and torsion in reinforced concrete", Struct. Eng. Mech., 77(5), 691-703. https://doi.org/10.12989/sem.2021.77.5.691.
  35. Rahal, K.N. and Collins, M.P. (1995), "Analysis of sections subjected to combined shear and torsion-A theoretical model", ACI Struct. J., 92(4), 459-469.
  36. Rahal, K.N. and Collins, M.P. (1996), "Simple model for predicting torsional strength of reinforced and prestressed concrete sections", ACI Struct. J., 93(6), 658-666.
  37. Sato, Y., Nagatomo, K. and Nakamura, Y. (2003), "Bond-strengthening hooks for RC members with 1300 MPa-class shear-reinforcing spirals", J. Asian Archit. Build. Eng., 2(2), 7-14.
  38. Shima, H., Chou, L.L. and Okamura, H. (1987), "Micro and macro models for bond in reinforced concrete", J. Faculty Eng., 39(2), 133-194.
  39. Tepfers, R. (1982), "Lapped tensile reinforcement splices", ASCE J. Struct. Div., 108(1), 283-301. https://doi.org/10.1061/JSDEAG.0005865
  40. Vecchio, F.J. and Collins, M.P. (1986), "The modified compression-field theory for reinforced concrete elements subjected to shear", ACI Struct. J., 83(2), 219-231.