We investigated the creep of concrete arches based on the following theories: the theory of linear creep by Harutyunyan-Maslov, kinetic theory, the theory of flow, theory of aging, and nonlinear theory of Y. Gurieva. We considered viscoelastic model of the concrete, ie total strain was represented as the sum of elastic strain and creep strain. Solution of the problem was carried out by finite element method. We considered the arch rigidly clamped at the ends and loaded with a uniformly distributed load. Graphs of growth of deflection and stress distribution in the reinforcement and concrete are represented. We obtained the substantial redistribution of stress between the reinforcement and the concrete during creep: in reinforcement stresses increased and in concrete stresses decreased. The strongest redistribution occurs on the theory Y. Gureva.

Keywords: reinforced concrete arch, creep theory of heredity, aging theory, the theory of flow, kinetic theory, finite element method, stress-strain state

The article presents basic equations for reinforced concrete elements that are experiencing bending moment and axial force, taking into account the creep of concrete. The stress-strain state of reinforced concrete statically determinate three–hinged arch is investigated on the basis of these equations. Also for this task we gained the resolving equations of finite element method and compared the numerical-analytical calculation with the numerical performed using the finite element method to the arch loaded with a uniformly distributed load and having the shape of a circular arc. The calculations used viscoelastic model, according to which the total deformation is the sum of concrete elastic deformation and creep. We consider a rectangular cross section with symmetrical reinforcement. It is shown that because of creep stress redistribution between concrete and reinforcement arises.

Keywords: finite element method, the creep of concrete, viscoelasticity, reinforced concrete arch, the stress–strain state.

The phenomenon of buckling under the creep of concrete arches was investigated. Solution of the problem carried out by means of the finite element method. To analyze the stability we used Newton-Raphson method. It has been established that there is a long-term critical load, beyond which the growth of the deflection has not fading character. As the equation of the relationship between the creep deformation and strains we used viscoelastoplastic hereditary model of aging concrete. To determine the creep strain we used a linear approximation with respect to time. It was found that the long critical load for considered arch was in 1.44 times lower than the instant critical load.

Keywords: reinforced concrete arch, stability, creep, geometric nonlinearity, finite element method, Newton-Raphson method