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Nonlinear section model for analysis of RC circular tower structures weakened by openings

Lechman, Marek    (Building Research Institute   ); Stachurski, Andrzej    (Institute of Control and Computation Engineering, Warsaw University of Technology  );
  • 초록

    This paper presents the section model for analysis of RC circular tower structures based on nonlinear material laws. The governing equations for normal strains due to the bending moment and the normal force are derived in the case when openings are located symmetrically in respect to the bending direction. In this approach the additional reinforcement at openings is also taken into account. The mathematical model is expressed in the form of a set of nonlinear equations which are solved by means of the minimization of the sums of the second powers of the residuals. For minimization the BFGS quasi-Newton and/or Hooke-Jeeves local minimizers suitably modified are applied to take into account the box constraints on variables. The model is verified on the set of data encountered in engineering practice. The numerical examples illustrate the effects of the loading eccentricity and size of the opening on the strains and stresses in concrete and steel in the cross-sections under consideration. Calculated results indicate that the additional reinforcement at the openings increases the resistance capacity of the section by several percent.


  • 주제어

    tower .   structure .   reinforced concrete .   opening .   box-constrained optimization.  

  • 참고문헌 (12)

    1. Bazaraa, M.S., Sherali, J. and Shetty, C.M. (1993), Nonlinear Programming. Theory and Algorithms, John Wiley and Sons, New York 
    2. Bertsekas, D.P. (1997), Nonlinear Programming, Athena Scientific, Belmont, Massachussets 
    3. CICIND (1998), Model Code for Concrete Chimneys 
    4. DIN 1056 (1984), Freistehende Schornsteine in Massivbauart 
    5. Fletcher, R. (1970), 'A new approach to variable metric algorithms', Computer Journal, 317-322 
    6. Fletcher, R. (1987), Practical Methods of Optimization, sec. ed., John Wiley and Sons, Chichester 
    7. Hooke, R. and Jeeves, T.A. (1961), 'Direct search solution of numerical and statistical problems', J. Association Computer Machinery, 212-229 
    8. Lechman, M. and Lewinski, P.M. (1994), 'The constitutive equations for nonlinear analysis of RC chimneys with non-circular cross-sections', Proc. of EURO-C 1994 Int. Conf. 'Computational Modelling of Concrete Structures', Ed. by H. Mang, N. Bicanic, R. de Borst, Innsbruck, 22nd-25th March 1994, Pineridge Press Ltd., 745-754 
    9. Lechman, M. and Lewinski, P.M. (2001), 'Generalized section model for analysis of reinforced concrete chimneys weakened by openings', Engineering Transactions, 1, 4-28 
    10. Nieser, H. and Engel, V. (1986), Industrieschornsteine in Massivbau, Beuth, Berlin 
    11. Pinfold, M. (1984), Reinforced Concrete Chimneys and Towers, sec. ed., Viewpoint Publications, London 
    12. Stachurski, A. and Wierzbicki, A.P. (2001), Introduction to Optimization, (Podstawy Optymalizacji, in Polish), sec. ed., Oficyna Wydawnicza Politechniki Warszawskiej, Warszawa 

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