Structural Engineering and Mechanics

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Direct kinematic method for exactly constructing influence lines of forces of statically indeterminate structures

  • Yang, Dixiong (Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology) ;
  • Chen, Guohai (Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology) ;
  • Du, Zongliang (Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology)
  • Received : 2014.08.31
  • Accepted : 2015.04.04
  • Published : 2015.05.25
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Abstract

Constructing the influence lines of forces of statically indeterminate structures is a traditional issue in structural engineering and mechanics. However, the existing kinematic method for establishing these force influence lines is an indirect or mixed approach by combining the force method with the theorem of reciprocal displacements, which is yet inconsistent with the kinematic method for statically determinate structure. This paper proposes the direct kinematic method in conjunction with the load-displacement differential relation for exactly constructing influence lines of reaction and internal forces of indeterminate structures. Firstly, through applying the principle of virtual displacement, the formula for influence lines of reaction and internal forces of indeterminate structure via direct kinematic method is derived based on the released structure. Then, a computational approach with a clear concept and unified procedure as well as wide applicability based on the load-displacement differential relation of beam is suggested to achieve conveniently the closed-form expression of force influence lines, and exactly draw them. Finally, three representative examples for constructing force influence lines of statically indeterminate beams and frame illustrate the superiority of the proposed method.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China

References

  1. Bhavikatti, S.S. (2005), Structural Analysis, 2nd Edition, Vikas Publishing House, New Delhi, India.
  2. Buckley, E. (1997), "Basic influence line equations of continuous beams and rigid frames", J. Struct. Eng., 123(10), 1416-1420. https://doi.org/10.1061/(ASCE)0733-9445(1997)123:10(1416)
  3. Buckley, E. (2003), The Influence Line Approach to the Analysis of Rigid Frames, Kluwer Academic Publishers, New York, USA.
  4. Chen, S.F. (2002), "Kinematic method for constructing influence line and theorem of reciprocal reactiondisplacement", Mech. Eng., 24(6), 59-61.
  5. Dowell, R.K. (2009), "Closed-form moment solution for continuous beams and bridge structures", Eng. Struct., 31, 1880-1887. https://doi.org/10.1016/j.engstruct.2009.03.012
  6. Dowell, R.K. and Johnson, T.P. (2011), "Shear and bending flexibility in closed-form moment solutions for continuous beams and bridge structures", Eng. Struct., 33, 3238-3245. https://doi.org/10.1016/j.engstruct.2011.08.016
  7. Ghali, A., Neville, A.M. and Brown, T.G. (2003), Structural Analysis: a Unified Classical and Matrix Approach, 5th Edition, Spon Press, New York, USA.
  8. Hibbeler, R.C. (2002), Structural Analysis, 5th Edition, Prentice Hall Inc, New Jersey, USA.
  9. Kassimali, A. (1999), Structural Analysis, 2nd Edition, Brooks/Cole Publishing Company, Pacific Grove, CA, USA.
  10. Kurrer, K.E. (2008), The History of the Theory of Structures: from Arch Analysis to Computational Mechanics, Ernst & Sohn Verlag, Berlin, Germany.
  11. Leet, K. and Uang, C.M. (2002), Fundamentals of Structural Analysis, 2nd Edition, McGraw-Hill, New York, USA.
  12. Li, L.K. (2010), Structural Mechanics, 5th edition, Higher Education Press, Beijing, China.
  13. Liu, S.M. and Wang, Q.H. (2001), "Problem and suggestion of kinematic method for drawing influence line of internal force of continuous beam", Mech. Eng., 23(2), 61-63.
  14. Long, Y.Q. and Bao, S.H. (2012), Structural Mechanics, 3rd Edition, Higher Education Press, Beijing, China.
  15. Strauss, A., Wendner, R., Bergmeister, K. and Frangopol, D.M. (2011), Monitoring and influence lines based performance indicators, Eds. Faber, Kohler and Nishijima, Applications of Statistics and Probability in Civil Engineering, Taylor & Francis Group, London, UK.
  16. Strauss, A., Wendner, R., Frangopol, D.M. and Bergmeister, K. (2012), "Influence line-model correction approach for the assessment of engineering structures using novel monitoring techniques", Smart Struct. Syst., 9(1), 1-20. https://doi.org/10.12989/sss.2012.9.1.001
  17. Thompson, F. and Haywood, C.G. (1986), Structural Analysis Using Virtual Work, Chapman and Hall Ltd, London, UK.
  18. Timoshenko, S.P. and Young, D.H. (1965), Theory of Structures, 2nd Edition, McGraw-Hill, New York, USA.
  19. Walls, R. and Elvin, A. (2010), "Optimizing structures subject to multiple deflection constraints and load cases using the principle of virtual work", J. Struct. Eng., 136(11), 1444-1452. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000246
  20. Yang, Y.B., Chen, C.T., Lin, T.J. and Hung, C.R. (2011), "Consistent virtual work approach for the nonlinear and postbuckling analysis of steel frames under thermal and mechanical loadings", Eng. Struct., 33(6), 1870-1882. https://doi.org/10.1016/j.engstruct.2011.02.005
  21. Zhao, H., Uddin, N., Shao, X.D., Zhu, P. and Tan, C.J. (2015), "Field-calibrated influence lines for improved axle weight identification with a bridge weigh-in-motion system", Struct. Infrastruct. Eng., 11(6), 721-743. https://doi.org/10.1080/15732479.2014.904383
  22. Zhu, S.Y., Chen, Z.W., Cai, Q.L., Lei, Y. and Chen, B. (2014), "Locate damage in long-span bridges based on stress influence lines and information fusion technique", Adv. Struct. Eng., 17(8), 1089-1102. https://doi.org/10.1260/1369-4332.17.8.1089