Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Multi-potential capacity for reinforced concrete members under pure torsion

  • Ju, Hyunjin (Department of Civil Engineering and Natural Hazards, University of Natural Resources and Life Sciences) ;
  • Han, Sun-Jin (Department of Architectural Engineering, University of Seoul) ;
  • Kim, Kang Su (Department of Architectural Engineering, University of Seoul) ;
  • Strauss, Alfred (Department of Civil Engineering and Natural Hazards, University of Natural Resources and Life Sciences) ;
  • Wu, Wei (Department of Civil Engineering and Natural Hazards, University of Natural Resources and Life Sciences)
  • Received : 2019.09.07
  • Accepted : 2020.03.05
  • Published : 2020.08.10
⟨ Previous Next ⟩

Abstract

Unlike the existing truss models for shear and torsion analysis, in this study, the torsional capacities of reinforced concrete (RC) members were estimated by introducing multi-potential capacity criteria that considered the aggregate interlock, concrete crushing, and spalling of concrete cover. The smeared truss model based on the fixed-angle theory was utilized to obtain the torsional behavior of reinforced concrete member, and the multi-potential capacity criteria were then applied to draw the capacity of the member. In addition, to avoid any iterative calculation in the existing torsional behavior model, a simple strength model was suggested that considers key variables, such as the effective thickness of torsional member, principal stress angle, and strain effect that reduces the resistance of concrete due to large longitudinal tensile strain. The proposed multi-potential capacity concept and the simple strength model were verified by comparing with test results collected from the literature. The study found that the multi-potential capacity could estimate in a rational manner not only the torsional strength but also the failure mode of RC members subjected to torsional moment, by reflecting the reinforcing index in both transverse and longitudinal directions, as well as the sectional and material properties of RC members.

Keywords

References

  1. ACI 318 (2014), Building Code Requirements for Structural Concrete and Commentary. American Concrete Institute, ACI 318R-14, Farmington Hills, MI, USA.
  2. Belarbi, A. and Hsu, T.T.C. (1991), "Constitutive Laws of Concrete in Biaxial Tension-Compression", Research Report UHCEE 91-2; Department of Civil and Environmental Engineering, University of Houston, Houston, Texas, 1-155.
  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. http://doi.org/10.14359/4154.
  4. Belarbi, A. and Hsu, T.T.C. (1995), "Constitutive Laws of Softened Concrete in Biaxial Tension-Compression", ACI Struct. J., 92(5), 562-573. http://doi.org/10.14359/907.
  5. Belletti, B., Cerioni, R. and Iori, I. (2001), "Physical Approach for Reinforced-Concrete (PARC) Membrane Elements", J. Struct. Eng., 127(12), 1412-1426. https://doi.org/10.1061/(ASCE)0733-9445(2001)127:12(1412).
  6. Belletti, B., Scolari, M. and Vecchi, F. (2017), "PARC_CL 2.0 Crack Model for NLFEA of Reinforced Concrete Structures under Cyclic Loadings", Comput. Struct., 191(1), 165-179. https://doi.org/10.1016/j.compstruc.2017.06.008.
  7. Bentz, E.C. and Collins, M.P. (2006), "Development of the 2004 Canadian Standards Association (CSA) A23.3 Shear Provisions for Reinforced Concrete", Canadian J. Civil Eng., 33(5), 521-534. http://doi.org/10.1139/L06-005.
  8. Bentz, E.C., Vecchio, F.J. and Collins, M.P. (2006), "Simplified Modified Compression Field Theory for Calculating Shear Strength of Reinforced Concrete Elements", ACI Struct. J., 103(4), 614-624. http://doi.org/10.14359/16438.
  9. Bishara, A. and Peir, J.C. (1968), "Reinforced Concrete Rectangular Columns in Torsion", J. Struct. Divison ASCE, 94(ST12), 2913-2933. https://doi.org/10.1061/JSDEAG.0002147
  10. Bredt, R. (1896), "Kritische Bemerkungen zur Drehungselastizitat. Z Vereines Deutscher Ingenieure", Band, 40(28), 785-790.
  11. Cerioni, R., Bernardi, P., Michelini, E. and Mordini, A. (2011), "A general 3D Approach for the Analysis of Multi-Axial Fracture Behavior of Reinforced Concrete Elements", Eng. Fracture Mech., 78(8), 1784-1793. https://doi.org/10.1016/j.engfracmech.2011.01.020.
  12. Chakraborty, M. (1977), "Torsional-Balanced Steel in Concrete Beams", J. ASCE Struct. Division, 103(ST11), 2181-2191. https://doi.org/10.1061/JSDEAG.0004765
  13. Chalioris, C.E. (2006), "Experimental Study of the Torsion of Reinforced Concrete Beams", Struct. Eng. Mech., 23(6), 713-737. https://doi.org/10.12989/sem.2006.23.6.713.
  14. Chen, W.F. (1982), Plasticity in Reinforced Concrete, McGraw-Hill, New York, USA.
  15. 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.
  16. Collins, M.P. and Mitchell, D. (1991), Prestressed Concrete Structures, Prentice-Hall, New Jersey, USA.
  17. CSA (1994), Design of concrete structures. A23.3-94, Canadian Standards Association, Etobicoke, Ontario, Canada.
  18. CSA (2004), Design of Concrete Structures, A23.3-04, Canadian Standards Association, Mississauga, Ontario, Canada.
  19. Elfgren, L., Karlsson, I. and Losberg, A. (1974), "Torsion-Bending-Shear Interaction for Concrete Beams", J. Struct. Divison ASCE, 100(ST8), 1657-1676. https://doi.org/10.1061/JSDEAG.0003843
  20. Fang, I.K. and Shiau, J.K. (2004), "Torsional Behavior of Normal- and High-Strength Concrete Beams", ACI Struct. J., 101(3), 304-313. http://doi.org/10.14359/13090.
  21. Goodno, B.J. and Gere, J.M. (2017), Mechanics of Materials, Cengage Learning, MA, USA.
  22. Greene, G.G. and Belarbi, A. (2009), "Model for Reinforced Concrete Members under Torsion, Bending, and Shear. I: Theory", J. Eng. Mech. ASCE, 135(9), 961-969. http://doi.org/10.1061/(ASCE)0733-9399(2009)135:9(961).
  23. Hwang, J.H., Lee, D.H., Ju, H., Kim, K.S., Kang, T.H.K. and Pan, Z.F. (2016), "Shear Deformation of Steel Fiber-Reinforced Prestressed Concrete Beams", J. Concrete Struct. Mater., 10(3), S53-S63. http://doi.org/10.1007/s40069-016-0159-2.
  24. Hsu TTC (1968), "Torsion of Structural Concrete-Behavior of Reinforced Concrete Rectangular Members", Torsion of Structural Concrete. American Concrete Institute, Farmington Hills, Detroit, USA, ACI Publications SP-18, 261-306. http://doi.org/10.14359/17572.
  25. Hsu, T.T.C. (1984), Torsion of Reinforced Concrete, Van Nostrand Reinhold, New York, USA.
  26. Hsu, T.T.C. (1990), "Shear Flow Zone in Torsion of Reinforced Concrete", J. Struct. Eng., 116(11), 3206-3226. https://doi.org/10.1061/(ASCE)0733-9445(1990)116:11(3206)
  27. Hsu, T.T.C. (1998), "Stresses and Crack Angles in Concrete Membrane Elements", J. Struct. Eng. ASCE, 124(12), 1476-1484. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:12(1476).
  28. Hsu, T.T.C. and Mo, Y.L. (1985), "Softening of concrete in torsional members-Theory and Tests", ACI J., 82(3), 290-303. http://doi.org/10.14359/10335.
  29. Hsu, T.T.C. and Mo, Y.L. (1985), "Softening of concrete in torsional members-Design Recommendations", ACI J., 82(4), 443-451. http://doi.org/10.14359/10355.
  30. Hsu, T.T.C. and Mo, Y.L. (2010), Unified Theory of Concrete Structures, Wiley and Sons, New York, USA.
  31. Hsu, T.T.C. and Zhang, L.X. (1996), "Tension Stiffening in Reinforced Concrete Membrane Element", ACI Struct. J., 93(1), 108-115. http://doi.org/10.14359/9681.
  32. Hsu, T.T.C. and Zhang, L.X. (1997), "Nonlinear analysis of membrane elements by fixed-angle softened-truss model", ACI Struct. J., 94(5), 483-492. http://doi.org/10.14359/498.
  33. Hsu, T.T.C. and Zhu, R.R.H. (2002), "Softened Membrane Model for Reinforced Concrete Elements in Shear", ACI Struct. J., 99(4), 460-469. http://doi.org/10.14359/12115.
  34. Jeng, C.H. (2015), "Unified Softened Membrane Model for Torsion in Hollow and Solid Reinforced Concrete Members: Modeling Precracking and Postcracking Behavior", J. Struct. Eng. ASCE, 141(10), 1-20. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001212.
  35. Jeng, C.H. and Hsu, T.T.C. (2009), "A Softened Membrane Model for Torsion in Reinforced Concrete Members", Eng. Struct., 32(9), 1944-1954. https://doi.org/10.1016/j.engstruct.2009.02.038.
  36. Ju, H., Kim, K.S., Lee, D.H., Hwang, J.H., Choi, S.H. and Oh, Y.H. (2015), "Torsional Responses of Steel Fiber-Reinforced Concrete Members", Compos. Struct., 129(1), 143-156. https://doi.org/10.1016/j.compstruct.2015.04.003.
  37. Ju, H., Lee, D.H. and Kim, K.S. (2019), "Minimum Torsional Reinforcement Ratio for Reinforced Concrete Members with Steel Fibers", Compos. Struct., 207(1), 460-470. https://doi.org/10.1016/j.compstruct.2018.09.068.
  38. Ju, H., Lee, D., Kim, J.R. and Kim, K.S. (2020), "Maximum Torsional Reinforcement Ratio of Reinforced Concrete Beams", Structures, 23(1), 481-493. https://doi.org/10.1016/j.istruc.2019.09.007.
  39. Ju, H., Lee, D.H., Hwang, J.H., Kim, K.S. and Oh, Y.H. (2013), "Fixed-Angle Smeared-Truss Approach with Direct Tension Force Transfer Model for Torsional Behavior of Steel Fiber-Reinforced Concrete Members", J. Adv. Concrete Technol., 11(9), 215-229. http://doi.org/10.3151/jact.11.215.
  40. Koutchoukali, N.E. and Belarbi, A. (2001), "Torsion of High-Strength Reinforced Concrete Beams and Minimum Reinforcement Requirement", ACI Struct. J., 98(4), 462-469. http://doi.org/10.14359/10289.
  41. Lee, J.Y. and Kim, S.W. (2010), "Torsional Strength of RC Beams Considering Tension Stiffening Effect", J. Struct. Eng. ASCE, 136(11), 1367-1378. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000237.
  42. Lee, D.H., Han, S.J. and Kim, K.S. (2016), "Dual Potential Capacity Model for Reinforced Concrete Beams Subjected to Shear", Struct. Concrete, 17(3), 1443-456. http://doi.org/10.1002/suco.201500165.
  43. Lessig, N.N. (1959), "Determination of the Load Carrying Capacity of Reinforced Concrete Elements with Rectangular Cross-Section Subjected to Flexure with Torsion", Institute Betona I Zhelezobetona, Moscow, Work 5, 4-28.
  44. Lu, J.K. and Wu, W.H. (2001), "Application of Softened Truss Model with Plastic Approach to Reinforced Concrete Beams in Torsion", Struct. Eng. Mech., 11(4), 393-406. https://doi.org/10.12989/sem.2001.11.4.393.
  45. McMullen, A.E. and El-Degwy, W.M. (1985), "Prestressed Concrete Tests Compared with Torsion Theories", PCI J., 30(5), 96-127. http://doi.org/10.15554/pcij.09011985.96.127.
  46. McMullen, A.E. and Rangan, B.V. (1978), "Pure Torsion in Rectangular Sections-A Re-Examination", ACI J., 75(10), 511-519. http://doi.org/10.14359/10963.
  47. Mitchell, D. and Collins, M.P. (1974), "Diagonal compression field theory-A rational model for structural concrete in pure torsion", ACI J., 71(8), 396-408. http://doi.org/10.14359/7103.
  48. Muttoni, A. and Fernandez, R.M. (2008), "Shear Strength of Members without Transverse Reinforcement as a Function of the Critical Shear Crack Width", ACI Struct. J., 105(2), 163-172. http://doi.org/10.14359/19731.
  49. Pang, X.B. and Hsu, T.T.C. (1996), "Fixed-angle softened-truss model for reinforced concrete", ACI Struct. J., 93(2), 197-207. http://doi.org/10.14359/1452.
  50. Rahal, K.N. (1993), "Behavior of Reinforced Concrete Beams Subjected to Combined Shear and Torsion", Ph.D. Dissertation, University of Toronto, Ontario, Canada.
  51. 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.
  52. Rahal, K.N. (2006), "Evaluation of AASHTO-LRFD General Procedure for Torsion and Combined Loading", ACI Struct. J., 103(5), 683-692. http://doi.org/10.14359/16920.
  53. 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. http://doi.org/10.14359/995.
  54. 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. http:/doi.org/10.14359/512.
  55. Rahal, K.N. and Collins, M.P. (1999), "Background to the General Method of Shear Design in the 1994 CSA-A23.3 Standard", Canadian J. Civil Eng., 26(6), 827-839. http://doi.org/10.1139/l99-050.
  56. Sherwood, E.G., Bentz, E.C. and Collins, M.P. (2007), "Effect of Aggregate Size on Beam-Shear Strength of Thick Slabs", ACI Struct. J., 104(2), 180-191. http://doi.org/10.14359/18530.
  57. Stevens, N.J., Uzumeri, S.M., Collins, M.P. and Will, G.T. (1991), "Constitutive Model for Reinforced Concrete Finite Element Analysis", ACI Struct. J., 88(1), 49-59. http://doi.org/10.14359/3105.
  58. Taylor, H.P.J. (1970), "Investigating of Forces Carried across Cracks in Reinforced Concrete Beams in Shear by Interlock of Aggregate", TRA 42.447; Cement and Concrete Association, London, United Kingdom. 1-22.
  59. Tsampras, G., Sause, R., Zhang, D., Fleischman, R., Restrepo, J., Mar, D. and Maffei, J. (2016), "Development of Deformable Connection for Earthquake-Resistant Buildings to Reduce Floor Accelerations and Force Responses", Earthq. Eng Struct. Dynam., 45(9), 1473-1494. http://doi.org/10.1002/eqe.2718.
  60. Vas Rodrigues, R.V., Muttoni, A. and Fernandez, R.M. (2010), "Influence of Shear on Rotation Capacity of Reinforced Concrete Members without Shear Reinforcement", ACI Struct. J., 107(5), 516-525. http://doi.org/10.14359/51663902.
  61. Vecchio, F.J. (2000), "Disturbed Stress Field Model for Reinforced Concrete: Formulation", J. Struct. Eng. ASCE, 126(9), 1070-1077. http://doi.org/10.1061/(asce)0733-9445(2000)126:9(1070).
  62. Vecchio, F.J. and Collins, M.P. (1982), "The Response of Reinforced Concrete to In-Plane Shear and Normal Stresses", Department of Civil Engineering, University of Toronto, Ontario, Canada, Publication 82-03, 1-332.
  63. Vecchio, F.J. and Collins, M.P. (1986), "The Modified Compression Field Theory for Concrete Elements Subjected to Shear", ACI J., 83(2), 219-231. http://doi.org/10.14359/10416.
  64. Vecchio, F.J. and Collins, M.P. (1988), "Predicting the Response of Reinforced Concrete Beams Subjected to Shear Using Modified Compression Field Theory", ACI Struct. J., 85(3), 258-268. http://doi.org/10.14359/2515.
  65. Vecchio, F.J. and Collins, M.P. (1993), "Compression Response of Cracked Reinforced Concrete", J. Struct. Eng. ASCE, 119(2), 3590-3610. http://doi.org/10.1061/(asce)0733-9445(1993)119:12(3590).
  66. Walrarven, J.C. (1981), "Fundamental Analysis of Aggregate Interlock", J. Struct. Divison ASCE, 107(ST11), 2245-2270. https://doi.org/10.1061/JSDEAG.0005820
  67. Watanabe, F. and Lee, J.Y. (1998), "Theoretical Prediction of Shear Strength and and Failure Mode of Reinforced Concrete Beams", ACI Struct. J., 95(6), 749-757. http://doi.org/10.14359/588.
  68. Wight, J.K. (2015), Reinforced Concrete Mechanics and Design, Pearson, New York, USA.
  69. Zhang, D., Kim, J., Tulebekova, S., Saliyev, D. and Lee, D.H. (2018), "Structural Responses of Reinforced Concrete Pile Foundations Subjected to Pressures from Compressed Air for Renewable Energy Storage", J. Concrete Struct. Mater., 12(74), 1-16. http://dor.org/10.1186/s40069-018-0294-z.