KSCE Journal of Civil and Environmental Engineering Research (대한토목학회논문집)

Korean Society of Civil Engeneers (대한토목학회)
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Fiber Finite Element Mixed Method for Nonlinear Analysis of Steel-Concrete Composite Structures

강-콘크리트 합성구조물의 비선형해석을 위한 화이버 유한요소 혼합법

  • 박정웅 (세종대학교 토목환경공학과) ;
  • 김승억 (세종대학교 토목환경공학과)
  • Received : 2007.09.18
  • Accepted : 2008.10.30
  • Published : 2008.11.30
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Abstract

The stiffness method provides a framework to calculate the structural deformations directly from solving the equilibrium state. However, to use the displacement shape functions leads to approximate estimation of stiffness matrix and resisting forces, and accordingly results in a low accuracy. The conventional flexibility method uses the relation between sectional forces and nodal forces in which the equilibrium is always satisfied over all sections along the element. However, the determination of the element resisting forces is not so straightforward. In this study, a new fiber finite element mixed method has been developed for nonlinear anaysis of steel-concrete composite structures in the context of a standard finite element analysis program. The proposed method applies the Newton method based on the load control and uses the incremental secant stiffness method which is computationally efficient and stable. Also, the method is employed to analyze the steel-concrete composite structures, and the analysis results are compared with those obtained by ABAQUS. The comparison shows that the proposed method consistently well predicts the nonlinear behavior of the composite structures, and gives good efficiency.

강성도법에서는 평형상태의 해석을 통해 구조물의 변위를 바로 산정할 수 있다. 그러나 변위형상함수를 사용하여 강성행렬과 부재내력의 계산이 근사적으로 수행되므로 유연도법에 비해 정확도가 낮은 단점이 있다. 종래의 유연도법에서는 변위형상 함수를 사용하지 않고 평형방정식을 만족하는 단면력-절점력 관계를 사용하여 단면력을 산정하므로 요소 내의 모든 단면에서 평형방정식을 만족시킬 수 있다. 그러나 유연도법은 강성도법에 비해 요소상태의 결정이 용이하지 않은 단점이 있다. 본 연구에서는 이러한 강성도법과 유연도법의 장점을 활용하여 강-콘크리트 합성구조물의 비선형해석을 위한 새로운 화이버 유한요소 혼합법(mixed method)을 개발하였다. 제안된 방법은 하중제어를 통한 Newton 방법을 사용하고 수치해석적으로 효과적이고 수렴성이 우수한 증분할선탄성계수법에 기반을 두고 있다. 또한 제안된 방법을 사용하여 강-콘크리트 합성구조물을 해석하였고 그 결과를 상용프로그램인 ABAQUS와 비교하였다. 그 결과 제안된 방법은 강-콘크리트 합성구조물의 비선형 거동을 정확하게 평가하였고 경제성이 매우 우수한 방법으로 입증되었다.

Keywords

References

  1. 김승억, 박주수(2002) 횡비틀림좌굴을 고려하는 2차 소성힌지해석을 이용한 3차원 강뼈대 구조물 설계, 한국전산구조공학회논문집, 한국전산구조공학회, Vol. 15, No. 1, pp. 117-125.
  2. 김승억, Ngo-Huu, C., 이동호(2005) 공간 강뼈대 구조물의 비선형 동적 해석, 한국전산구조공학회논문집, 한국전산구조공학회, Vol. 18, No. 4, pp. 395-404.
  3. 조창근, 권민호, 정희효(2005) 변단면 형강 부재의 파이버 유한 요소 비선형 정밀해법 알고리즘, 대한토목학회논문집, 대한토목학회, 제25권 제4A호, pp. 611-619.
  4. ABAQUS Standard Version 6.5 User Manual. (2005).
  5. Chen, W.F. and Kim, S.E. (1997) LRFD steel design using advanced analysis. Boca Raton, FL. CRC Press.
  6. Foster, S.J. and Gilbert, R.I. (1996) The design of nonflexural members with normal and high-strength concretes, ACI Structural Journal, Vol. 93, No. 1, pp. 3-10.
  7. Hajjar, J.F. (2002) Composite steel and concrete structural systems for seismic engineering, Journal of Constructional Steel Research, Vol. 58, No. 5-8, pp. 703-723. https://doi.org/10.1016/S0143-974X(01)00093-1
  8. Hajjar, J.F., Molodan, A., and Schiller, P.H. (1998a) A distributed plasticity model for cyclic analysis of concrete-filled steel tube beam-columns and composite frames, Engineering Structures, Vol. 20, No. 4-6, pp. 398-412. https://doi.org/10.1016/S0141-0296(97)00020-5
  9. Hajjar, J.F., Schiller, P.H., and Molodan, A. (1998b) A distributed plasticity model for concrete-filled steel tube beam-columns with interlayer slip, Engineering Structures, Vol. 20, No. 8, pp. 663-676. https://doi.org/10.1016/S0141-0296(97)00107-7
  10. Hjelmstad, K. and Taciroglu. E. (2002) Mixed methods and flexibility approaches for nonlinear frame analysis, Journal of Constructional Steel Research, Vol. 58, pp. 967-993. https://doi.org/10.1016/S0143-974X(01)00100-6
  11. Hjelmstad, K. and Taciroglu. E. (2003) Mixed variational methods for finite element analysis of geometrically non-linear, inelastic Bernoulli-Euler beams, Communication in Numerical Methods in Engineering, Vol. 19, pp. 809-832. https://doi.org/10.1002/cnm.622
  12. Hsu, T.T.C. and Zhang, L.X.B. (1997) Nonlinear analysis of membrane elements by fixed-angle softened-truss model, ACI Structural Journal, Vol. 94, No. 5, pp. 483-492.
  13. Kent, D.C. and Park, R. (1971) Flexural members with confined concrete, Journal of the Structural Division, ASCE, Vol. 97, pp. 1964-1990.
  14. Kim, S.E., Lee, J., and Park, J.S. (2002) 3-D second-order plastichinge analysis accounting for lateral torsional buckling, International Journal of Solids and Structures, Vol. 39, No. 8, pp. 2109-2128. https://doi.org/10.1016/S0020-7683(02)00082-3
  15. Kim, S.E., Lee, J., and Park, J.S. (2003) 3-D second-order plastichinge analysis accounting for local buckling, Engineering Structures, Vol. 25, No. 1, pp. 81-90. https://doi.org/10.1016/S0141-0296(02)00122-0
  16. Kim, S.E. and Choi, S.H. (2005) Practical second-order inelastic analysis for three-dimensional steel frames subjected to distributed load, Thin-Walled Structures, Vol. 43, No. 1, pp. 135-160. https://doi.org/10.1016/j.tws.2004.09.001
  17. Kim, S.E. and Ngo-Huu, C. (2006) Practical advanced analysis software for Space Steel Structure Design, Steel Structures, Vol. 6, pp. 107-120.
  18. Lee, J. and Fenves, G.L. (1998) Plastic-damage model for cyclic loading of concrete structures, Journal of Engineering Mechanics, ASCE, Vol. 124, No. 8, pp. 892-900. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:8(892)
  19. Lubliner, J., Oliver, J., Oller, S., and Onte, E. (1989) A plasticdamage model for concrete, Int. J. of Solids and Structures, Vol. 25, No. 3, pp. 229-326.
  20. Petrangeli, M. and Ciampi V. (1997) Equilibrium based iterative solution for the non-linear beam problem, Int. J. for Numerical Methods in Engineering, Vol. 40, pp. 423-437. https://doi.org/10.1002/(SICI)1097-0207(19970215)40:3<423::AID-NME72>3.0.CO;2-H
  21. Spacone, E., Ciampi, V., and Filippou, F.C. (1996) Mixed formulation of nonlinear beam finite element, Computer & Structures, Vol. 58, No. 1, pp. 71-83. https://doi.org/10.1016/0045-7949(95)00103-N
  22. Spacone, E., Filippou, F.C., and Taucer, F.F. (1996a) Fibre beam column model for nonlinear analysis of R/C frames. Part I: Formulation, Earthquake Engineering and Structural Dynamics, Vol. 25, pp. 711-725. https://doi.org/10.1002/(SICI)1096-9845(199607)25:7<711::AID-EQE576>3.0.CO;2-9
  23. Spacone, E., Filippou, F.C., and Taucer, F.F. (1996b) Fibre beam column model for nonlinear analysis of R/C frames. Part II: Applications. Earthquake Engineering and Structural Dynamics, Vol. 25, pp. 727-742. https://doi.org/10.1002/(SICI)1096-9845(199607)25:7<727::AID-EQE577>3.0.CO;2-O
  24. Vecchio, F.J. (1990) Reinforced concrete membrane element formulations, ASCE Journal of Structural Engineering, Vol. 116, No. 3, pp. 730-750. https://doi.org/10.1061/(ASCE)0733-9445(1990)116:3(730)
  25. Vecchio, F.J. and Collins, M.P. (1986). Modified compression field theory for reinforced concrete elements subjected to shear, ACI J. Proceedings, Vol. 83, No. 2, pp. 219-231.