DOI QR코드

DOI QR Code

An Indeterminate Strut-Tie Model and Load Distribution Ratio for Reinforced Concrete Corbels

철근콘크리트 코벨의 부정정 스트럿-타이 모델 및 하중분배율

  • 채현수 (경북대학교 건축토목공학부) ;
  • 윤영묵 (경북대학교 건축토목공학부)
  • Received : 2013.02.17
  • Accepted : 2013.12.06
  • Published : 2014.08.01

Abstract

The ultimate behavior of reinforced concrete corbel is complicated due to the primary design variables including the shear span-to-effective depth ratio a/d, flexural reinforcement ratio, load condition, and material properties. In this study, a simple indeterminate strut-tie model reflecting all characteristics of the ultimate strength and complicated structural behavior is proposed for the design of the reinforced concrete corbels with shear span-to-effective depth ratio of $a/d{\leq}1$. A load distribution ratio, defined as the fraction of applied load transferred by horizontal truss mechanism, is also proposed to help structural designers perform the design of reinforced concrete corbels by using the strut-tie model approaches of current design codes. For the development of the load distribution ratio, numerous material nonlinear finite element analyses of the proposed indeterminate strut-tie model were conducted by changing primary design variables. The ultimate strengths of reinforced concrete corbels tested to failure were evaluated by incorporating the proposed strut-tie model and load distribution ratio into the ACI 318-11's strut-tie model method. The validity of the proposed model and load distribution ratio was examined by comparing the strength analysis results with those by the ACI 318-11's conventional design method and strut-tie model methods of current design codes.

철근콘크리트 코벨의 파괴거동은 코벨의 전단경간비 및 주인장 철근비를 포함한 여러 변수들로 인해 복잡하다. 이 논문에서는 철근콘크리트 코벨의 강도 및 거동 특성을 논리적이고 합리적인 방법으로 반영하여 전단경간비가 1.0 이하인 철근콘크리트 코벨을 설계할 수 있는 단순한 형태의 1차 부정정 트러스 구조의 스트럿-타이 모델을 제안하였다. 또한 부정정 스트럿-타이 모델을 정정 트러스 구조의 스트럿-타이 모델로 변환시켜 현행 스트럿-타이 모델 설계기준에 의한 코벨의 설계를 가능하게 하는 하중분배율을 제안하였다. 하중분배율 결정 시 스트럿과 타이의 재료적 비선형 거동을 고려할 수 있는 부정정 스트럿-타이 모델의 비탄성 구조해석을 통해 철근콘크리트 코벨의 강도 및 거동을 지배하는 전단경간비, 주인장 철근비, 수직하중에 대한 수평하중의 비, 그리고 콘크리트의 압축강도 등의 주요설계변수들의 영향을 반영하였다. 이 연구에서 제안한 부정정 스트럿-타이 모델 및 하중분배율의 적합성을 검증하기 위해 파괴실험이 수행된 다수의 철근콘크리트 코벨의 극한강도를 평가하였으며, 그 결과를 ACI 318-11의 전통적인 설계기준 및 정정 트러스 구조의 스트럿-타이 모델을 기반으로 하는 현행 주요 설계기준의 스트럿-타이모델 방법에 의한 평가결과와 비교분석하였다.

Keywords

References

  1. ACI Subcommittee 445 (2002). Examples for the design of structural concrete with strut-and-tie models; SP-208, American Concrete Institute, Farmington Hills, Michigan, USA.
  2. Ali, M. A. and White, R. N. (2001). "Consideration of compression stress bulging and strut degradation in truss modeling of ductile and brittle corbels."Engineering Structures, Vol. 23, pp. 240-249. https://doi.org/10.1016/S0141-0296(00)00040-7
  3. American Association of State Highway and Transportation Officials (2010). AASHTO LRFD bridge design specifications, 5 th Edition, Washington, D.C., USA.
  4. American Concrete Institute (2011). Building code requirements for structural concrete (ACI 318M-11) and commentary, Farmington Hills, Michigan, USA.
  5. Bergmeister, K., Breen, J. E., Jirsa, J. O. and Kreger, M. E. (1993). Detailing in structural concrete, Research Report 1127-3F, University of Texas at Austin, Texas, USA.
  6. Campione, G. (2009). "Flexural response of FRC corbels."Cement & Concrete Composites, Vol. 31, 2009, pp. 204-210. https://doi.org/10.1016/j.cemconcomp.2009.01.006
  7. Canadian Standards Association (CSA) (2004). Design of concrete structures for buildings, A23.3-M04, Rexdale, Ontario, Canada.
  8. Chae, H. S. (2012). Indeterminate strut-tie models for reinforced concrete deep beams and corbels, Ph.D Dissertation, Kyungpook National University, Daegu, Korea, p. 290.
  9. Collins, M. P. and Mitchell, D. (2001). Prestressed concrete structures, 3 rd Edition, Prentice Hall, Englewood Cliffs, New Jersey, p. 766.
  10. Comite Euro-International du Beton (2010). CEP-FIP model code 2010, International Federation for Structural Concrete (fib), Lausanne, Switzerland.
  11. European Committee for Standardization (2004). Eurocode 2: Design of Concrete Structures, Brussels, Belgium.
  12. Fattuhi, N. I. (1994). "Reinforced corbels made with plain and fibrous concretes."ACI Structural Journal, Vol. 91, No. 5, pp. 530-536.
  13. Fattuhi, N. I. and Hughes, B. P. (1989). "Ductility of reinforced concrete corbels containing either steel fibers or stirrups."ACI Structural Journal, Vol. 86, No. 6, pp. 644-651.
  14. Foster, S. J., Powell, R. E. and Selim, H. S. (1996). "Performance of high-strength concrete corbels."ACI Structural Journal, Vol. 93, No. 5, pp. 555-563.
  15. Hermansen, B. R. and Cowan, J. (1974). "Modified shear-friction theory for bracket design."ACI Journal, Proceedings, Vol. 71, No. 1, pp. 55-60.
  16. Hwang, S. J., Lu, W. Y. and Lee, H. J. (2000). "Shear strength prediction for reinforced concrete corbels."ACI Structural Journal, Vol. 97, No. 4, pp. 543-552.
  17. Jensen, B. C. (1979). "Reinforced concrete corbels - Some Exact Solutions, Final report, IABSE colloquium on plasticity in reinforce concrete."International Association for Bridge and Structural Engineering, Zurich, Vol. 29, No. 2, pp. 293-300.
  18. Jensen, B. C. (1982). "On the ultimate load of reinforced concrete corbels, Dialog I-82."Miscellaneous Papers in Civil Engineering, Danish Engineering Academy, Lyngby, pp. 119-137.
  19. Korean Concrete Institute (KCI) (2012). Specifications for design of concrete members, Kimoon-dang, p. 342.
  20. Korean Concrete Institute (KCI) (2013). Strut-tie model design examples of structural concrete, Kimoon-Dang, p. 259.
  21. Kriz, L. B. and Raths, C. H. (1965). "Connections in precast concrete structures - strength of corbels."PCI Journal, Vol. 10, No. 1, pp. 16-61. https://doi.org/10.15554/pcij.02011965.16.61
  22. Mast, R. F. (1968). "Auxiliary reinforcement in concrete connections." Proceedings, ASCE, Vol. 94, No. 6, pp. 1485-1504.
  23. Mattock, A. H., Chen, K. C. and Soongswang, K. (1976). "The behavior of reinforced concrete corbels."PCI Journal, Vol. 21, No. 2, pp. 52-77. https://doi.org/10.15554/pcij.03011976.52.77
  24. Nawy, E. G., Stark, H. and Opaluch, W. (2011). Prestressed concrete: A Fundamental Approach, Pearson Prentice Hall, Upper Saddle River, New Jersey, USA, p. 984.
  25. Pang, X. B. and Hsu, T. T. C. (1995). "Behavior of reinforced concrete membrane elements in shear."ACI Structural Journal, Vol. 92, No. 6, pp. 665-679.
  26. Rogowsky, D. M. and MacGregor, J. G. (1983). Shear strength of deep reinforced concrete beams, Structural Engineering Report No. 110, Department of Civil Engineering, University of Alberta, Edmonton, USA, p. 178.
  27. Russo, G., Venir, R., Pauletta, M. and Somma, G. (2006). "Reinforced concrete corbels."ACI Structural Journal, Vol. 103, No. 1, pp. 3-10.
  28. Shaikh, A. F. (1978). "Proposed revisions to shear-friction provisions." PCI Journal, Vol. 23, No. 1, pp. 12-21.
  29. Solanki, H. and Sabnis, G. M. (1987). "Reinforced concrete corbels - simplified."ACI Structural Journal, Vol. 84, pp. 428-432.
  30. Wight, J. K., Richart, F. E. and MacGregor, J. G. (2011). Reinforced concrete: Mechanics and Design, 5 th Edition, Prentice Hall, Englewood Cliffs, New Jersey, USA, p. 1157.
  31. Yong, Y. K. and Balaguru, P. (1994). "Behavior of reinforced high-strength concrete corbels."Journal of Structural Engineering, ASCE, Vol. 120, No. 5, pp. 1182-1201. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:4(1182)
  32. Yun, Y. M. (2005). "Effective strength of concrete strut in strut-tie model (I): Methods for determining effective strength of concrete strut."Journal of the Korean Society of Civil Engineers, Vol. 25, No. 1A, pp. 49-59.
  33. Yun, Y. M. and Ramirez, J. A. (1994). "Strut-Tie model design of disturbed regions in concrete structure."ASCE Structural Congress XII, Atlanta, Georgia, USA.
  34. Yun, Y. M., Kim, B. H., Lee, W. S. and Jeong, C. H. (2007). "Prediction of shear strength for reinforced concrete corbels using shear-friction and strut-tie models."Journal of the Korean Society of Civil Engineers, Vol. 27, No. 2, pp. 141-155.
  35. Zhang, L. X. B. and Hsu, T. T. C. (1998). "Behavior and analysis of 100MPa concrete membrane elements."Journal of Structural Engineering, ASCE, Vol. 124, No. 1, pp. 24-34. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:1(24)

Cited by

  1. Prediction of Failure Strength of Reinforced Concrete Deep Beams using Two-dimensional Grid Strut-Tie Model Method vol.36, pp.4, 2016, https://doi.org/10.12652/Ksce.2016.36.4.0605