Computers and Concrete

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Numerical method for the strength of two-dimensional concrete struts

  • Yun, Y.M. (School of Architectural, Civil, Environmental and Energy Engineering, Kyungpook National University)
  • Received : 2020.11.23
  • Accepted : 2021.12.17
  • Published : 2021.12.25
⟨ Previous Next ⟩

Abstract

For the reliable strut-and-tie model (STM) design of disturbed regions of concrete members, structural designers must accurately determine the strength of concrete struts to check the strength conditions of a selected STM el and the anchorage of reinforcing bars in nodal zones. In this study, the author proposed a consistent numerical method for strut strength, applicable to all two-dimensional STMs. The proposed method includes the effects of a biaxial stress state associated with tensile strains in reinforcing bars crossing a strut, deviation angle between strut orientation and compressive principal stress flow, and degree of confinement provided by reinforcement. The author examined the method's validity through the STM prediction of the ultimate strengths of 517 reinforced concrete (RC) deep beams, 24 RC panels, and 258 RC corbels, all tested to failure.

Keywords

Acknowledgement

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2018R1D1A1B06041177).

References

  1. ASHTO (2014), AASHTO LRFD Bridge Design Specifications, 7th Ed., Washington, DC, USA.
  2. AASHTO (2018), AASHTO LRFD Bridge Design Specifications, 8th Ed., Washington, DC, USA.
  3. Abdul-Razzaq, K.S. and Dawood A.A. (2020), "Corbel strut and tie modeling-Experimental verification", Struct., 26, 327-339. https://doi.org/10.1016/j.istruc.2020.04.021.
  4. ACI (2019), Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary, Farmington Hills, MI, USA.
  5. ACI Subcommittee 445 (2002), Examples for the Design of Structural Concrete with Strut-and-Tie Models, SP-208, American Concrete Institute, Farmington Hills, MI, USA.
  6. ACI-ASCE Committee 445 (2010), Further Examples for the Design of Structural Concrete with Strut-and-Tie Models, SP273, American Concrete Institute, Farmington Hills, MI, USA.
  7. Ahmad, S., Shah, A., Zaman, A. and Salimullah, K. (2011), "Design and evaluation of the shear strength of deep beams by strut and tie model (STM)", Transac. Civil Envir. Eng., 35(C1), 1-13.
  8. Alshegeir, A. (1992), "Analysis and design of disturbed regions with strut-and-tie models", Ph.D. Dissertation of Philosophy, Purdue University, West Lafayette, IN, USA.
  9. Anderson, N.S. and Ramirez, J.A. (1989), "Detailing of stirrup reinforcement", ACI Struct. J., 86(5), 507-515.
  10. Arabzadeh, A., Aghayari, R. and Rahai, A.R. (2011), "Investigation of experimental and analytical shear strength of reinforced concrete deep beams", Int. J. Civil Eng., 9(3), 207-214.
  11. Bergmeister, K., Breen, J.E. and Jirsa, J.O. (1991), "Dimensioning of the nodes and development of reinforcement", IABSE Colloquium Report, International Association for Bridge and Structural Engineering.
  12. Bergmeister, K., Breen, J.E. and Jirsa, J.O. (1991), "Dimensioning of the nodes and development of reinforcement", IABSE Colloquium, International Association for Bridge and Structural Engineering.
  13. Brena, S.F. and Roy, N.C. (2009), "Evaluation of load transfer and strut strength of deep beams with short longitudinal bar anchorages", ACI Struct. J., 106(5), 678-689.
  14. Brown, M.D., Sankovich, C.L., Bayrak, O. and Jirsa, J.O. (2006), "Behavior and efficiency of bottle-shaped Struts", ACI Struct. J., 103(3), 348-355.
  15. Chae, H.S. (2012), "Indeterminate strut-tie models for reinforced concrete deep beams and corbels", Ph.D. Dissertation of Philosophy, Kyungpook National University, Daegu, Korea.
  16. Chen, H., Yi, W.J. and Hwang, H.J. (2018), "Cracking strut-and-tie model for shear strength evaluation of reinforced concrete deep beams", Eng. Struct., 163, 396-408. https://doi.org/10.1016/j.engstruct.2018.02.077.
  17. Chetchotisak, P., Yindeesuk, S. and Teerawong, J. (2017), "Interactive strut-and-tie-model for shear strength prediction of RC pile caps", Comput. Concrete, 20(3), 329-338. https://doi.org/10.12989/cac.2017.20.3.329.
  18. Collins, M.P. and Mitchell, D. (1980), "Design proposals for shear and torsion", J. Prestress. Concrete Inst., 25(5), 70.
  19. CSA (2014), Design of Concrete Structures CSA A23.3-14, Rexdale, ON, Canada.
  20. European Committee for Standardization (2004), Eurocode 2: Design of Concrete Structures, Brussels, Belgium.
  21. Fattuhi, N.I. (1994), "Reinforced corbels made with plain and fibrous concretes", ACI Struct. J., 91(5), 530-536.
  22. fib (2010), CEP-FIP model code 2010, Comite Euro-International du Beton, Lausanne, Switzerland.
  23. Foster, S.J., Powell, R.E. and Selim, H.S. (1996), "Performance of high-strength concrete corbels", ACI Struct. J., 93(5), 555-563.
  24. Foster, S.J. and Gilbert, R.I. (1998), "Experimental studies on high-strength concrete deep beams", ACI Struct. J., 95(4), 382-390.
  25. Khosravikia, F., Kim, H.S., Yi, Y., Wilson, H.R., Yousefpour, H., Hrynyk, T. and Bayrak, O. (2018), "Experimental and numerical assessment of corbels designed based on strut-and-tie provisions", J. Struct. Eng., 144(9), 04018138. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002137.
  26. Hussein, G., Sayed, S.H., Nasr, N.E. and Mostafa, A.M. (2018), "Effect of loading and supporting area on shear strength and size effect of concrete deep beams", Ain Shams Eng. J., 9, 2823-2831. https://doi.org/10.1016/j.asej.2017.11.002.
  27. Kim, W. and Jeong, J. (2011), "Decoupling of arch action in shear-critical reinforced concrete beams", ACI Struct. J., 108(4), 395-404.
  28. Kim, S.C. and Park, S.Y. (2005), "A study on shear steel effect on RC deep beams", J. Korean Soc. Civil Eng., 25(2), 365-374.
  29. Kim, B.H. and Yun, Y.M. (2011), "An indeterminate strut-tie model and load distribution ratio for RC deep beams-(I) model and load distribution ratio", Adv. Struct. Eng., 14(6), 1031-1041. https://doi.org/10.1260/1369-4332.14.6.1031.
  30. Kriz, L.B. and Raths, C.H. (1965), "Connections in precast concrete structures-Strength of corbels", PCI J., 10(1), 16-61. https://doi.org/10.15554/pcij.02011965.16.61
  31. Lee, J.Y., Choi, I.J. and Kim, S.W. (2011), "Shear behavior of reinforced concrete beams with high-strength stirrups", ACI Struct. J., 108(5), 620-629.
  32. Lim, E. and Hwang, S.J. (2016), "Modeling of the strut-and-tie parameters of deep beams for shear strength prediction", Eng. Struct., 108, 104-112. https://doi.org/10.1016/j.engstruct.2015.11.024.
  33. Lu, W.Y., Lin, I.J, and Yu, H.W. (2013), "Shear strength of reinforced concrete deep beams", ACI Struct. J., 110(4), 671-680.
  34. MacGregor, J.G. (1997), Reinforced Concrete-Mechanics and Design, 4th Ed., Prentice Hall, Englewood Cliffs, NJ, USA.
  35. Marti, P. (1985), "Basic tools of reinforced concrete beam design", J. Am. Concrete Inst., 82(1), 46-56.
  36. Mattock, A.H., Chen, K.C. and Soongswang, K. (1976), "The behavior of reinforced concrete corbels", PCI J., 21(2), 52-77. https://doi.org/10.15554/pcij.03011976.52.77
  37. Mustafa, T.S., Beshara, F.B.A., Mahmoud, A.A. and Khalil, M.A. (2019), "An improved strut-and-tie model to predict the ultimate strength of steel fiber-reinforced concrete corbels", Mater. Struct., 52, 63. https://doi.org/10.1617/s11527-019-1363-8.
  38. Muttoni, A., Ruiz, M.F. and Niketic, F. (2015), "Design versus assessment of concrete structures using stress fields and strut-and-tie models", ACI Struct. J., 112(5), 605-616. https://doi.org/10.14359/51687710.
  39. Nielsen, M.P., Braestrup, M.W., Jensen, B.C. and Bach, F. (1978), "Concrete plasticity, beam shear-shear in joints-punching shear", Spec. Pub., 1-129.
  40. Oh, J.K. and Shin, S.W. (2001), "Shear strength of reinforced high-strength concrete deep beams", ACI Struct. J., 98(2), 164-173.
  41. O zkal, F.M. and Uysal, H. (2017), "Reinforcement detailing of a corbel via an integrated strut-and-tie modeling approach", Comput. Concrete, 19(5), 589-597. https://doi.org/10.12989/cac.2017.19.5.589.
  42. Panjehpour, M., Chai, H.K. and Voo, Y.L. (2015), "Refinement of strut-and-tie model for reinforced concrete deep beams", PloS One, 10(6). https://doi.org/10.1371/journal.pone.0130734.
  43. Parol, J., Al-Qazweeni, J. and Salam, S.A. (2018), "Analysis of reinforced concrete corbel beams using strut and tie models", Comput. Concrete, 21(1), 95-102. https://doi.org/10.12989/cac.2018.21.1.095.
  44. PCA (2004), AASHTO LRFD Strut-Tie Model Design Examples, Skokie, IL, USA.
  45. Quintero-Febres, C.G., Parra-Montesinos, G. and Wight, J.K. (2006), "Strength of struts in deep concrete members designed using strut-and-tie method", ACI Struct. J., 103(4), 577-586.
  46. Ramirez, J.A. and Breen, J.E. (1983), "Proposed design procedure for shear and torsion in reinforced and prestressed concrete", 248-4F, University of Texas.
  47. 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.
  48. Sarsam, K.F. and Al-Musawi, J.M.S. (1992), "Shear design of high- and normal strength concrete beams with web reinforcement", ACI Struct. J., 89(6), 658-664.
  49. Schlaich, J., Schaefer, K. and Jennewein, M. (1987), "Towards a consistent design of structural concrete", J. Prestress. Concrete Inst., 32(3), 74-151.
  50. Shin, S.W., Lee, K.S., Moon, J. and Ghosh, S.K. (1999), "Shear strength of reinforced high-strength concrete beams with shear span-to-depth ratios between 1.5 and 2.5", ACI Struct. J., 96(4), 549-556.
  51. Smith, K.M. and Vantsiotis, A.S. (1982), "Shear strength of deep beams", ACI Mater. J., 79(3), 201-213.
  52. Sumpter, M.S., Rizkalla, S.H. and Zia, P. (2009), "Behavior of high-performance steel as shear reinforcement for concrete beams", ACI Struct. J., 106(2), 171-177.
  53. Tan, K.H., Kong, F.K., Teng, S. and Guan, L. (1995), "High-strength concrete deep beams with effective span and shear span variations", ACI Struct. J., 92(4), 572-582.
  54. Tan, K.H., Kong, F.K., Teng, S. and Weng, L.W. (1997a), "Effect of web reinforcement on high-strength concrete deep beams", ACI Struct. J., 94(6), 572-582.
  55. Tan, K.H., Teng, S., Kong, F.K. and Lu, H.Y. (1997b), "Main tension steel in high strength concrete deep and short beams", ACI Struct. J., 94(5), 752-768.
  56. Tan, K.H. and Lu, H.Y. (1999), "Shear behavior of large reinforced concrete deep beams and code comparisons", ACI Struct. J., 96(5), 836-845.
  57. Tanimura, Y. and Sato, T. (2005), "Evaluation of shear strength of deep beams with stirrup", QR Railway Tech. Res. Inst., 46(1), 53-58. https://doi.org/10.2219/rtriqr.46.53.
  58. Teng, S., Kong, F.K., Poh, S.P., Guan, L.W. and Tan, K.H. (1996), "Performance of strengthened concrete deep beams predamaged in shear", ACI Struct. J., 93(2), 159-171.
  59. Thurlimann, B. (1976), "Shear strength of reinforced and prestressed concrete-CEB approach", Spec. Pub., 59, 93-116.
  60. Tran, C.T.C., Nguyen, X.H., Nguyen, H.C. and Vu, N.S. (2020), "Strut-and-tie model for shear capacity of corroded reinforced concrete columns", Adv. Concrete Constr., 10(3), 185-193. https://doi.org/10.12989/acc.2020.10.3.185.
  61. Xie, Y., Ahmad, S.H., Yu, T., Hino, S. and Chung, W. (1994), "Shear ductility of reinforced concrete beams of normal and high-strength concrete", ACI Struct. J., 91(2), 140-149.
  62. Yang, K.H., Chung, H.S., Lee, E.T. and Eun, H.C. (2003), "Shear characteristics of high-strength concrete deep beams without shear reinforcements", Eng. Struct., 25, 1343-1352. https://doi.org/10.1016/S0141-0296(03)00110-X.
  63. Zhang, N. and Tan, K.H. (2007), "Size effect in RC deep beams: Experimental investigation and STM verification", Eng. Struct., 29, 3241-3254. https://doi.org/10.1016/j.engstruct.2007.10.005.