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Comparison of calculation results for beam finite element model of the structure and model from two-dimensional elements

In the determination of stressedly-deformed state of solid building structures using a finite element method, different approaches to building of finite element models may be used. In each particular case, the degree of model elaboration is selected on the basis of conditions formulated in the statement of problem.

Consider two different approaches to building of a solid finite element model by example of cover structure of Odintsovo Volleyball Center.
The finite element model is required to perform the following calculations of the structure under permanent (proper weight) and superimposed loads:
etermination of stressedly-deformed state in the bearing elements of the structure,

determination of local stresses at the connection points of bearing structures.

The cover of the Center is the system of cross girders from roll-formed welded closed sections.

General view of the structure

Connections of bearing elements in the joints are realized by two methods: edge lines of roll-formed welded sections are welded to the plates, and these welded sections are joined together with high-strength bolts.

Joint with an element of bolted joint

For this problem, two finite element models of the structure cover were developed:

1. Beam finite element model
In the beam model, the sections are modeled by one-dimensional bend elements with specified characteristics of beam sections. Owing to its simple building, this is the most wide-spread method of solid building structure modeling. Besides, to determine the characteristics of bearing elements (beams and posts) at the design stage, the results of beam model calculation will be sufficient.

Fragment of beam finite element model of cover structure

2. The second finite element model is formed with the use of two-dimensional elements (SHELL elements). In this case, solid geometry of sections and structural features of connection points with account taken of thicknesses of all structural elements are modeled in sufficient detail. Subject to importance of the structure, smaller details may be modeled (nonstandard bolted joints, welded joints, etc). Modern computers make it possible to calculate a complete model of the structure allowing the designer to see the picture of stressed state of the structure in its entirety.

Fragment of finite element model from two-dimensional elements

For both finite element models, calculations were made with loading of the structure by specified forces. Both geometric and physical nonlinearity was taken into consideration.

Distribution of maximum principal stress in the beam model

Distribution of maximum principal stress in the detailed finite element model from two-dimensional elements

Distribution of minimum principal stress in the beam model

Distribution of minimum principal stress in the detailed finite element model from two-dimensional elements

The calculations showed coincidence of deflections in the structure with accuracy of 2% and coincidence of respective stresses in the bearing beams with accuracy of less than 3%. This makes it possible to draw a conclusion on adequacy of the models: the beam finite element model and the finite element model from two-dimensional elements. However, such coincidence of stresses is observed only in a significant distance from beam ends, while the values and nature of stress distribution at the connection points of the beams received in the calculation for detailed SHELL model are significantly different from the stresses which can be observed with the application of beam theory. In addition, it seems impossible to detect some local stress surges in the beam model.

The examples of local stress surges that cannot be detected by beam model calculation are described below.

Hexa Company to order of the State Unitary Enterprise of the Moscow Region, Mosoblstroyproject Design Institute, 2006

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