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

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

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