# Deformation calculation of space reinforced concrete frame by FEM with allowance for vibrocreep of concrete

## Authors

• Serhii Slobodianiuk Prydniprovska State Academy of Civil Engineering and Architecture, Ukraine
• Andrii Buratynskyi Prydniprovska State Academy of Civil Engineering and Architecture, Ukraine

## Keywords:

space frame, stiffness matrix, finite element method, algorithm, shrinkage, creep, concrete vibrocreep

## Abstract

The efficiency of the reinforced frameworks depends to a large extent on a properly framing scheme. If the framing scheme is made of reinforced concrete, the frame displays at various long static and dynamic loads such a characteristic phenomenon as the creep and vibrocreep of concrete. In addition, the space frame must take into account the buckling strain. An algorithm for the calculation of n-times kinematicly indeterminate space reinforced concrete frames has been developed, taking into account buckling strain, creep and vibrocreep based on finite element analysis and recursion formulas, which makes it possible to simplify the calculation of bar systems for long processes. Recursion formulas can be used to develop programs for calculating space frames. The article presents the research and obtained a stiffness matrix of three types of reinforced concrete space finite element, taking into account buckling strain and long processes. An algorithm for calculating reinforced concrete bar systems was developed taking into account the space work, buckling strain, vibocreep of concrete by finite element method. An executed example of the calculation of a reinforced concrete space framed structure showed that taking into account the buckling strain of the rods and the vibrocreep of concrete significantly alter the stress-strain state of space systems. Some frame motions increase by 135-348% over time, and the force variation varies from + 88% to -231% in comparison with elastic non-deformation values. The increase in displacements is mainly influenced by creep and vibration creep, which account for 135% –184% and 228% - 338%, respectively, and for the growth of efforts – buckling strain, the share of which ranged from + 10% to -228%. Deformation calculations of framed reinforced concrete systems should be performed not only to establish a change in the pattern of internal forces and time motions, but in the most dangerous places of the system to determine the stresses in reinforced and concrete and deflections to prevent the excess of calculated resistances of materials and normative motions.

## Author Biographies

### Serhii Slobodianiuk, Prydniprovska State Academy of Civil Engineering and Architecture

Doctor of Technical Sciences, Professor, Head of the Department of Theoretical Mechanics

### Andrii Buratynskyi, Prydniprovska State Academy of Civil Engineering and Architecture

Candidate of Technical Sciences, Associate Professor

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