DESIGNING AND DETAILING OF BUILDING SYSTEMS.MECHANICS IN CIVIL ENGINEERING

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
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  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.

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Solid models of rectangular section columns within the framework of analysis of building structures using the method of finite elements

Vestnik MGSU 9/2012
  • 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 .
  • Vasilev Aleksey Viktorovich - Rodnik Limited Liability Company design engineer 8 (482) 2-761-004, Rodnik Limited Liability Company, 22 Kominterna st., Tver, 170000, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 55 - 59

The theory of the strength of materials has produced a substantial influence on the development
and practical implementation of computer methods of the strength analysis of beams and
beam systems. Beams are modeled through the employment of one-dimensional elements within
the overwhelming majority of the finite element method software programmes; the stiffness matrix
is derived on the basis of the hypothesis of flat sections, and end forces concentrate in the centres
of the gravity of cross sections. This approach makes it possible to develop effective algorithms,
although it has several drawbacks. They include an incorrect transmission of forces from beams
to plates and massive elements of structures, difficulties in taking account of the warping effect of
the beam, and the complexity of taking account of physical and geometrical nonlinearities. Some
authors suggest using the three-dimensional theory with account for the flat sections hypothesis. It
encompasses the patterns of rotations of sections in the analysis of structures, although the problems
of warping and shear deformations remain.
The authors propose a new approach to rectangular column modeling by means of the finite
element analysis of building structures. Each column is presented as a set of three-dimensional
8-node elements with arbitrary discretization alongside the cross section and the height of the column.
The inner nodes of the finite element mesh are excluded sequentially layer by layer, thus,
reducing the stiffness matrix and other characteristics of the column with reference to its top and
bottom cross sections. The finite element method has been adapted to PRINS software programme.
The comparative analysis of the two structures has been completed with the help of this software.
The structures exposed to the structural analysis included slabs and columns. In one case,
columns were modeled with the help of one-dimensional elements, and in the another case, the
proposed elements were used. The comparison of the results demonstrates that the employment
of the proposed elements makes it possible to avoid problems associated with the transmission of
the force in a particular point.

DOI: 10.22227/1997-0935.2012.9.55 - 59

References
  1. Filin A.P. Matritsy v statike sterzhnevykh sistem [Matrices in the Statics of Framework Structures]. Ìoscow-Leningrad, Izd-vo literatury po stroitel’stvu publ. [Publishing House of Civil Engineering Literature]. 1966, 438 p.
  2. Rabotnov Yu.N. Soprotivlenie materialov [Strength of Materials]. Moscow, Fizmatgiz Publ., 1962, 456 p.
  3. Feodos’ev V.I. Soprotivlenie materialov [Strength of Materials]. Moscow, Nauka Publ., 1986, 512 p.
  4. Aleksandrov A.V., Lashchennikov B.Ya., Shaposhnikov N.N., Smirnov V.A. Metody rascheta sterzhnevykh sistem, plastin i obolochek s primeneniem EVM [Computer Methods of Analysis of Framework Structures, Plates and Shells]. Moscow, 1976.
  5. Kornoukhov N.V. Prochnost’ i ustoychivost’ sterzhnevykh sistem [Strength and Stability of Framework Structures]. Moscow, Stroyizdat Publ., 1949, 376 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. Ayoub À., Filippou F.C. Mixed Formulation of Nonlinear Steel-concrete Composite Beam Element. J. Structural Engineering. ASCE, 2000.
  9. Hjelmstad K.D., Taciroglu E. Mixed Variational Methods for Finite Element Analysis of Geometrically Non-linear, Inelastic Bernoulli-Euler Beams. Communications in Numerical Methods in Engineering. 2003.
  10. Agapov V.P. Issledovanie prochnosti prostranstvennykh konstruktsiy v lineynoy i nelineynoy postanovkakh s ispol’zovaniem vychislitel’nogo kompleksa «PRINS» [Strength Analysis of Three-dimensional Linear and Non-linear Structures Using PRINS Software Programme]. Collection of works “Threedimensional Constructions of Buildings and Structures: Research, Analysis, Design and Application”. no. 11, Moscow, 2008, pp. 57—67.

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