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.

Download

SUPERELEMENT OF A COLUMN HAVING A RECTANGULAR CROSS SECTION AND CHARACTERIZED BY PHYSICAL NONLINEARITY

Vestnik MGSU 5/2013
  • Agapov Vladimir Pavlovich - Moscow State University of Civil Engineering (MGSU) Doctor of Technical Sciences, Professor departmet of applied mechanics and mathematics; +7 (495) 583-47-52, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation.
  • Vasil’ev Aleksey Viktorovich - Rodnik Limited Liability structural engineer; +7 (482)276-10-04., Rodnik Limited Liability, 22 Kominterna St., 170000, Tver, Russian Federation.

Pages 29-34

They cause mistakes in the transfer of forces in specific points and invariability of sizes and types of cross sections of rods in the course of their deformation. The approach to the analysis of rectangular section columns is proposed. The new approach originates from the three-dimensional theory supplemented by the superelement technology. The column is divided into sections and finite elements. The analysis of physically nonlinear structures is executed using the PRINS software. The flow theory is used to identify the characteristics of finite elements. Huber-Mises plasticity criterion is applied. The console beam loaded by concentrated forces on the free end is calculated to verify the element. The limiting load value identified by PRINS software complies with the theoretical values derived using the theory of limit equilibrium.

DOI: 10.22227/1997-0935.2013.5.29-34

References
  1. NASTRAN Theoretical Manual. NASA, Washington, 1972.
  2. Basov Ê.À. ANSYS. Spravochnik pol’zovatelya [ANSYS. User Manual]. Moscow, DMK-Press Publ., 2005, 637 p.
  3. Bathe K.J., P.M. Wiener. On Elastic-plastic Analysis of I-Beams in Bending and Torsion. Computers and Structures. 1983, vol. 17, pp. 711—718.
  4. Barabash M.S., Genzerskiy Yu.V., Marchenko D.V. LIRA 9.2. Primery rascheta i proektirovaniya. Ch. 1 [LIRA 9.2. Examples of Analysis and Design. Part 1]. Kiev, FAKT Publ., 2005, 84 p.
  5. Filin A.P. Matritsy v statike sterzhnevykh system [Matrixes in the Statics of a Bar System]. Moscow-Leningrad, Izd-vo literatury po stroitel’stvu publ., 1966, 438 p.
  6. Zienkiewicz O.C., Taylor R.L. The Finite Element Method for Solid and Structural Mechanics. McGraw-Hill, 2005, 631 p.
  7. Bathe K.J. Finite Element Procedures. Prentice Hall, Inc., 1996, 1037 p.
  8. Agapov V.P. Issledovanie prochnosti prostranstvennykh konstruktsiy v lineynoy i nelineynoy postanovkakh s ispol’zovaniem vychislitel’nogo kompleksa «PRINS» [Study of Linear and Non-linear Strength of 3D Structures Using PRINS Software]. Prostranstvennye konstruktsii zdaniy i sooruzheniy (issledovanie, raschet, proektirovanie, primenenie) [3D Constructions of Buildings and Structures (study, analysis, design, application)]. Collection of works, edited by Shugaev V.V. Moscow, 2008, no. 11, pp. 57—67.
  9. Agapov V.P., Vasil’ev A.V. Modelirovanie kolonn pryamougol’nogo secheniya ob”emnymi elementami s ispol’zovaniem superelementnoy tekhnologii [Modeling of Rectangular Section Columns Using 3D Elements Backed by Theory of Superelements]. Stroitel’naya mekhanika inzhenernykh konstruktsiy i sooruzheniy [Structural Mechanics of Engineering Constructions and Structures]. 2012., no. 4, pp. 48—54.
  10. Rzhanitsyn A.R. Raschet sooruzheniy s uchetom plasticheskikh svoystv materialov [Analysis of Structures with Account for Plastic Properties of Materials]. Moscow, Gos. izd-vo literatury po stroitel’stvu i arkhitekture publ., 1954, 288 p.

Download

Results 1 - 2 of 2