DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

Account for geometrical nonlinearity in the analysis of reinforced concrete columns of rectangular section by finite element method

Vestnik MGSU 4/2014
  • Agapov Vladimir Pavlovich - Moscow State University of Civil Engineering (MGSU) Doctor of Technical Sciences, Professor, Department of Applied Mechanics and Mathematics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoye shosse, Moscow, 129337, Russian Federation; +7 (495) 583-47-52; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Vasil'ev Aleksey Viktorovich - limited liability company "Rodnik" design engineer, limited liability company "Rodnik", 22 Kominterna str., Tver, 170000, Russian Federation; +7 (482) 2-761-004; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 37-43

The superelement of a column of rectangular section made of homogeneous material and intended for linear analysis, developed by authors earlier on the basis of the three-dimensional theory of elasticity, is updated with reference to static analysis of reinforced concrete columns with account for geometrical nonlinearity. In order to get the superelement the column is divided on sections and longwise into eight-node solid finite elements modelling the concrete and two nodes rod elements modelling reinforcement. The elements are connected with one another in the nodes of finite element mesh that provides joint operation of concrete and reinforcement. The internal nodes of the obtained finite element mesh are excluded at the stage of stiffness matrix and load vector of a column calculation. Formulas for calculation of linearized stiffness matrix of a superelement and a vector of the nodal forces statically equivalent to internal stresses are received. The element is adjusted to the computer program PRINS, and can be used for geometrically nonlinear analysis of complex structures containing reinforced concrete columns of rectangular section. Separately standing reinforced concrete column was calculated on longitudinal-transverse bending for the verification of the received superelement. The critical load was determined according to the results of calculation. The determined critical force value corresponds to the theoretical value. Thus, the proposed method of accounting for the geometric nonlinearity in the analysis of reinforced concrete columns can be recommended for practical use.

DOI: 10.22227/1997-0935.2014.4.37-43

References
  1. Geniev G.A., Kissyuk V.N., Tyupin G.A. Teoriya plastichnosti betona i zhelezobetona [Plasticity Theory of Concrete and Reinforced Concrete]. Moscow, Stroyizdat Publ., 1974, 316 p.
  2. Yashin A.V. Kriterii prochnosti i deformirovaniya betona pri prostom nagruzhenii dlya razlichnykh vidov napryazhennogo sostoyaniya [Strength and Strain Criteria of Concrete at Simple Loading for Various Kinds of the Stress State]. Raschet i proektirovanie zhelezobetonnykh konstruktsiy [Analysis and Design of Reinforced Concrete Structures]. Moscow, 1977, pp. 48—57.
  3. Karpenko N.I. Obshchie modeli mekhaniki zhelezobetona [General Models of Reinforced Concrete Mechanics]. Moscow, Stroyizdat Publ., 1996, 396 p.
  4. Chen W.F. Plasticity in Reinforced Concrete. J. Ross Publishing, 2007. 463 p.
  5. Gedolin L., Deipoli S. Finite Element Studies of Shear-critical R/C Beams. ASCE Journal of the Engineering Mechanics Division. 1977, vol. 103, no. 3, pp. 395—410.
  6. Ngo D., Scordelis A.C. Finite Element Analysis of Reinforced Concrete. J. Am. Conc. Inst., 1967, vol. 64, pp. 152—163.
  7. Kotsovos M.D. Effect of Stress Path on the Behaviour of Concrete under Triaxial Stress States. J. Am. Conc. Inst., vol. 76, no. 2, pp. 213—223.
  8. Nam C.H., Salmon C.G. Finite Element Analysis of Concrete Beams. ASCE J. Struct. Engng. Div. Vol. 100, no. ST12, pp. 2419—2432.
  9. Willam, K.J., Warnke E.P. (1975). Constitutive Models for the Triaxial Behavior of Concrete. Proceedings of the International Assoc. for Bridge and Structural Engineering. Vol. 19, pp. 1—30.
  10. Hinton E., Owen D.R.J. Finite Element Software for Plates and Shells. Pineridge Press, Swansea, U.K., 1984, 403 pp.
  11. Beglov A.D., Sanzharovskiy R.S. Teoriya rascheta zhelezobetonnykh konstruktsiy na prochnost' i ustoychivost'. Sovremennye normy i Evrostandarty [The Theory of Strength and Buckling Analysis of the Reinforced Concrete Structures. Modern Norms and Eurostandards]. Saint Petersburg, Moscow, ASV Publ., 2006, 221 p.
  12. Mailyan D.R., Muradyan V.A. K metodike rascheta zhelezobetonnykh vnetsentrenno szhatykh kolonn [The Method of Calculating Eccentrically Compressed Reinforced Concrete Columns]. Inzhenernyy vestnik Dona [The Engineering Bulletin of Don]. 2012, no. 4 (part 2). Available at: http://www.ivdon.ru/magazine/archive/n4p2y2012/1333.
  13. Agapov V.P., Vasil'ev A.V. Modelirovanie kolonn pryamougol'nogo secheniya ob"emnymi elementami s ispol'zovaniem superelementnoy tekhnologii [Modeling Columns of Rectangular Cross-section with Superelement Technology]. Stroitel'naya mekhanika inzhenernykh konstruktsiy i sooruzheniy [Structural Mechanics of Engineering Buildings and Structures]. 2012, no. 4, pp. 48—53.
  14. Agapov V.P. Issledovanie prochnosti prostranstvennykh konstruktsiy v lineynoy i nelineynoy postanovkakh s ispol'zovaniem vychislitel'nogo kompleksa «PRINS» [Strength Analysis of Three-dimensional Structures with Computer Program PRINS]. Prostranstvennye konstruktsii zdaniy i sooruzheniy (issledovanie, raschet, proektirovanie, primenenie): sbornik statey [Three-dimensional Structures of Buildings (Investigation, Calculation, Design, Application): Collection of Articles]. Moscow, 2008, no. 11, pp. 57—67.
  15. Agapov V.P., Vasil'ev A.V. Superelement kolonny pryamougol'nogo secheniya s geometricheskoy nelineynost'yu [Superelement of the Rectangular Cross Section Column Having Physical Nonlinearity]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2013, no. 6, pp. 50—56.

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