DOI QR코드

DOI QR Code

Indeterminate Strut-Tie Model and Load Distribution Ratio of Continuous RC Deep Beams (I) Proposal of Model & Load Distribution Ratio

연속지지 RC 깊은 보의 부정정 스트럿-타이 모델 및 하중분배율 (I) 모델 및 하중분배율의 제안

  • Kim, Byung-Hun (Infrastructure Dept., HyunDai Engineering Co. Ltd.) ;
  • Chae, Hyun-Soo (School of Architecture & Civil Engineering, Kyungpook National University) ;
  • Yun, Young-Mook (School of Architecture & Civil Engineering, Kyungpook National University)
  • 김병헌 (현대엔지니어링 기반시설부) ;
  • 채현수 (경북대학교 건축토목공학부) ;
  • 윤영묵 (경북대학교 건축토목공학부)
  • Received : 2010.02.03
  • Accepted : 2010.10.12
  • Published : 2011.02.28

Abstract

The structural behavior of continuous reinforced concrete deep beams is mainly controlled by the mechanical relationships associated with the shear span-to-effective depth ratio, flexural reinforcement ratio, load and support conditions, and material properties. In this study, a simple indeterminate strut-tie model which reflects characteristics of the complicated structural behavior of the continuous deep beams is presented. In addition, the reaction and load distribution ratios defined as the fraction of load carried by an exterior support of continuous deep beam and the fraction of load transferred by a vertical truss mechanism, respectively, are proposed to help structural designers for the analysis and design of continuous reinforced concrete deep beams by using the strut-tie model approaches of current design codes. In the determination of the load distribution ratio, a concept of balanced shear reinforcement ratio requiring a simultaneous failure of inclined concrete strut and vertical steel tie is introduced to ensure a ductile shear failure of reinforced concrete deep beams, and the primary design variables including the shear span-to-effective depth ratio, flexural reinforcement ratio, and concrete compressive strength are implemented after thorough parametric numerical analyses. In the companion paper, the validity of the presented model and load distribution ratio was examined by applying them in the evaluation of the ultimate strength of multiple continuous reinforced concrete deep beams, which were tested to failure.

철근콘크리트 깊은 보의 거동은 전단경간비, 휨철근비, 하중점과 지지점의 조건, 그리고 사용재료의 성질 등의 여러 변수간의 복합적인 역학관계로 인해 매우 복잡하다. 이 논문에서는 이러한 깊은 보의 거동 특성을 모두 반영하여 연속지지 철근콘크리트 깊은 보의 설계를 수행할 수 있는 부정정 스트럿-타이 모델을 제안하였다. 또한 현 스트럿-타이 모델 설계기준을 부정정 스트럿-타이 모델을 이용한 연속지지 철근콘크리트 깊은 보의 설계에 합리적으로 적용하기 위해 외부하중에 대한 단부 지지점 반력의 비인 반력분배율과 수직 트러스 메커니즘에 의해 전달되는 외부하중의 크기 즉 부정정 스트럿-타이 모델의 하중분배율을 제안하였다. 하중분배율의 결정 시 연속지지 철근콘크리트 깊은 보의 전단에 대한 연성파괴거동을 확보하기 위하여 깊은 보의 전단저항 메커니즘을 구성하는 콘크리트 스트럿과 수직철근타이가 동시에 파괴된다는 전단평형철근비 개념을 도입하였으며, 다양한 수치해석 결과를 바탕으로 연속지지 깊은 보의 강도 및 거동에 영향을 미치는 전단경간비, 휨철근비, 그리고 콘크리트의 압축강도 등의 주요설계변수를 고려하였다. 이 논문의 후속편에서는 기존의 여러 설계방법들과 이 연구에서 제안한 방법을 이용하여 파괴실험이 수행된 다양한 종류의 연속지지 깊은 보의 강도를 평가하고, 이 연구에서 제안한 방법의 적합성을 검증하였다.

Keywords

References

  1. Hwang, S. J., Lu, W. Y., and Lee, H. J., “Shear Strength Prediction for Deep Beams,” ACI Structural Journal, Vol. 97, No. 3, 2000, pp. 367-376.
  2. Foster, S. J. and Malik, A. R., “Evaluation of Efficiency Factor Models Used in Strut-and-Tie Model,” Journal of Structural Engineering, ASCE, Vol. 128, No. 5, 2002, pp. 569-577. https://doi.org/10.1061/(ASCE)0733-9445(2002)128:5(569)
  3. Hwang, S. J. and Lu, W. Y., “Strength Prediction for Discontinuity Regions by Softened Strut-and-Tie Model,” Journal of Structural Engineering, ASCE, Vol. 128, No. 12, 2002, pp. 1519-1526. https://doi.org/10.1061/(ASCE)0733-9445(2002)128:12(1519)
  4. Matamoros, A. B. and Wong, K. H., “Design of Simply Supported Deep Beams Using Strut-and-Tie Models,” ACI Structural Journal, Vol. 100, No. 6, 2003, pp. 704-712.
  5. Quintero-Febres, C. G., Parra-Montesinos, G., and Wight, J. K., “Strength of Struts in Deep Concrete Members Designed Using Strut-and-Tie Method,” ACI Structural Journal, Vol. 103, No. 4, 2006, pp. 577-586.
  6. Park, J. W. and Kuchma, D. A., “Strut-and-Tie Model Analysis for Strength Prediction of Deep Beams,” ACI Structural Journal, Vol. 104, No. 6, 2007, pp. 657-666.
  7. Tjhin, T. N. and Kuchma, D. A., “Integrated Analysis and Design Tool for the Strut-and-Tie Model,” Engineering Structure, Vol. 29, No. 11, 2007, pp. 3042-3052. https://doi.org/10.1016/j.engstruct.2007.01.032
  8. Ashour, F. and Yang, K. H., “Application of Plasticity Theory to Reinforced Concrete Deep Beams: A Review,” Magazine of Concrete Research, Vol. 60, No. 9, 2008, pp. 657-664. https://doi.org/10.1680/macr.2008.00038
  9. Canadian Standards Association, Design of Concrete Structures for Buildings, CAN3-A23.3-M84, Rexdale, Ontario, Canada, 1984, 281 pp.
  10. Concrete Design Committee, The Design of Concrete (NZS 3101: Part I and II), New Zealand Standard, New Zealand, 1995.
  11. British Standards Institution, Code of Practice for Design and Construction (BS8110 Part I), British Standard, UK, 1997, 120 pp.
  12. The International Federation for Structural Concrete (fib), Structural Concrete; Textbook on Behavior, Design and Performance Updated Knowledge of the CEB/FIP Model Code 1999 Volume 3, The International Federation for Structural Concrete(fib), Lausanne, Switzerland, 1999, 292 pp.
  13. American Association of State Highway and Transportation Officials, AASHTO LRFD Bridge Design Specifications, 4th Edition, Washington, DC, USA, 2007, pp. 5-1-5-264.
  14. American Concrete Institute, Building Code Requirements for Structural Concrete (ACI 318M-08) and Commentary, Farmington Hills, Michigan, USA, 2008, 473 pp.
  15. Alshegeir, A., Analysis and Design of Disturbed Regions with Strut-Tie Models, Ph.D Dissertation, School of Civil Engineering, Purdue University, West Lafayette, Indiana, USA, 1992. 273 pp.
  16. MacGregor, J. G., Reinforced Concrete: Mechanics and Design, 3rd Edition, Prentice-Hall, New Jersey, USA, 1997, 938 pp.
  17. ACI Subcommittee 445-1, Examples for the Design for Structural Concrete with Strut-and-Tie Models; SP-208, Reineck R. H. eds, American Concrete Institute, Michigan, USA, 2002, 242 pp.
  18. Foster, S. J. and Gilbert, R. I., “Experimental Studies on High-Strength Concrete Deep Beams,” ACI Structural Journal, Vol. 95, No. 4, 1998, pp. 382-390.
  19. 김병헌, 윤영묵, “단순지지 RC 깊은 보 부정정 스트럿-타이 모델의 하중분배율- (I) 하중분배율의 제안,” 대한토목학회 논문집, 28권, 2A호, 2008, pp. 259-267.
  20. 김병헌, 정찬핵, 윤영묵, “단순지지 RC 깊은 보 부정정스트럿-타이 모델의 하중분배율- (II) 적합성 평가,” 대한토목학회 논문집, 28권, 2A호, 2008, pp. 269-279.
  21. Rogowsky, D. M., MacGregor, J. G., and Ong, S. Y., “Tests of Reinforced Concrete Deep Beams,” ACI Structural Journal, Vol. 83, No. 4, 1986, pp. 614-623.
  22. Ashour, A. F., “Tests of Reinforced Concrete Continuous Deep Beams,” ACI Structural Journal, Vol. 94, No. 1, 1997, pp. 3-12.
  23. Pang, X. B. and Hsu, T. T. C., “Behavior of Reinforced Concrete Membrane Elements in Shear,” ACI Structural Journal, Vol. 92, No. 6, 1995, pp. 665-679.
  24. Leonhardt, F., “Reducing the Shear Reinforcement in Reinforced Concrete Beams and Slabs,” Magazine of Concrete Research, Vol. 17, No. 53, 1965, pp. 187-198. https://doi.org/10.1680/macr.1965.17.53.187
  25. Park, R. and Paulay, T., Reinforced Concrete Structures, John Wiley & Sons, New York, USA, 1970, 769 pp.
  26. 김우, 정제평, 김대중, “휨과 전단이 작용하는 RC 부재의 해석을 위한 비-베르누이-적합 트러스 모델링 기법 연구(I),” 대한토목학회 논문집, 23권, 6호, 2003, pp. 1247-1256.
  27. 김우, 정제평, 박대성, “휨과 전단이 작용하는 RC 부재의 해석을 위한 비-베르누이-적합 트러스 모델링 기법 연구(II),” 대한토목학회 논문집, 23권, 6호, 2003, pp. 1257~1266.
  28. Zsutty, T. C., “Shear Strenght Prediction for Separate Categories of Simple Beam Tests,” ACI Journal, Vol. 68, No. 2, 1971, pp. 138-143.
  29. Okamura, H. and Higai, T, “Proposed Design Equation for Shear Strength of R.C. Beams without Web Reinforcement,” Proceeding of Japan Society of Civil Engineering, 1980, pp. 131-141.
  30. Niwa, J., Yamada, K., Yokozawa, K., and Okamura, M., “Revaluation of the Equation for Shear Strength of R.C.-Beams without Web Reinforcement,” Proceeding of Japan Society of Civil Engineering, 1986, pp. 1986-1988.
  31. Eurocode 2, Design of Concrete Structures, Part I: General Rules and Rules for Buildings(DD ENV 1992-1-1), Commission of the European Communities, UK, 1992, 176 pp.
  32. Bazant, Z. P., “Fracturing Truss Model: Size Effect in Shear Failure of Reinforced Concrete,” Journal of Engineering Mechanics, ASCE, Vol. 123, No. 12, 1997, pp. 1276-1288. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:12(1276)
  33. American Concrete Institute, Building Code Requirements for Structural Concrete (ACI 318-99) and Commentary (ACI 318R-99), Farmington Hills, Michigan, USA, 1999, 391 pp.