Examples of Testing a Program for Modeling Long-Term Deformation of Prestressed Reinforced Concrete Beams

Introduction. Currently, there is very little information in the Russian literature on the development and practical application of numerical methods for studying the stress-strain state of concrete and reinforced concrete structures, taking into account the creep of concrete. As a rule, when analyzing the long-term deformation of such structures, calculators apply an empirical approach based on the use of the reduced modulus of deformation in combination with the coefficient of creep. The purpose of this study is to verify and validate the developed finite element algorithm and the corresponding software based on the results of experimental studies of the stress-strain state, prestressed reinforced concrete beam structures, taking into account the creep of concrete, available in the literature.

Materials and Methods. As a mathematical tool for modeling the process of long-term deformation of reinforced concrete girder structures, the finite element method was used in combination with a simple procedure for numerical integration along the time coordinate of the operator-matrix resulting equation. The program code is implemented on the basis of the Microsoft Visual Studio computing platform and the Intel Parallel Studio XE compiler with the built-in Intel Visual Fortran Composer XE text editor. The processes of storing and processing working arrays are implemented in terms of sparse matrices. The descriptive graphics of the Matlab computer system were used to visualize the calculation results. All of the computational experiments were performed using the authorized Polygon complex. The objectives of the study include evaluating the accuracy of the proposed methodology for analyzing the long-term deformation of reinforced concrete structures with various methods of external force action, including the effect of prestressing.

Results. A program for calculating reinforced concrete beam structures in a three-dimensional formulation has been developed and debugged using a discrete reinforcement scheme, according to which the reinforcing frame is modeled by rod (beam), and the concrete array by volumetric finite elements. To determine the restoring force caused by the tension of the cable reinforcement on concrete, a two-dimensional finite element model consisting of truss and spring finite elements is used. The simulation of long-term deformation was performed within the framework of the theory of linear viscoelasticity in combination with the principle of superimposition of influences.

Discussion and Conclusion. A comparative analysis of the results of field and computational experiments on the stressstrain state of reinforced concrete beams of rectangular cross-section with post- and prestress is performed. The proposed method makes it possible to calculate prestressed reinforced concrete girder structures with variable quasi-static loading, taking into account the linear creep of concrete.

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