Vol 18, No 6 (2022): Scientific Legacy of Academician Vitaly Mikhailovich Bondarenko

The problems of non-equilibrium and nonlinear processes in the evaluation of reinforced concrete structural systems robustness potential in ultimate states are considered. The definition of concept of “robustness exposition” is given for a quantitative assessment of the robustness potential. A calculation model based on the generalization of the well-known classical relationship between the current relative deficit change rate of the reinforced concrete stress-strain state with respect to each fixed time value is proposed to describe in time non-equilibrium processes of structural materials force resistance depending on the mode and level of loading. On the basis of the linear creep theory, aging materials, an algorithm was developed to determine the measure of creep, corrosion-damaged concrete and reinforced concrete and to determine the parameter “robustness exposition” of a reinforced concrete statically indeterminate structural system, taking into account non-equilibrium and nonlinear processes of its deformation in time. An example of a single-span rigidly clamped reinforced concrete beam calculating the robustness potential from the position of a special limiting state criterion is considered.

The authors deal with the structures of buildings in the form of shallow shells with some damage. The derivation of equations is given taking into account the geometric nonlinearity of the work of a thin-walled structure. A technique for solving systems of equations using the Bubnov - Galyorkin method is given. The work of the structure with various ways of fixing the edges is simulated. Damage is specified by changing the modulus of elasticity in an arbitrary section of the structure. The influence of the shape and location of the defect on the value of the critical load is investigated. The results of the studies carried out are given in a dimensionless form and illustrated by graphs, which makes it convenient to use them in engineering calculations. Recommendations are given for correcting the shape and thickness of coating structures in the form of shallow shells in order to maintain their bearing capacity in the event of defects. The proposed method can be used to determine and investigate the stress-strain state of structures in the form of shallow shells, taking into account the geometric nonlinearity of work in the presence of defects in them. The constructed graphs of the dependence of the critical load on various parameters make it possible to evaluate the operation of structures, taking into account changes in various factors at various stages of the structure's operation. The use of varying characteristics of the reduction in the modulus of elasticity, which appears because of the occurrence of a defect, shows results that are close to real conditions.

The calculation and prediction of the long-term safety of building structures is associated with the dynamics of the stress state of their composite elements and leads to relaxation problems for assessing the redistribution of stresses between the components that make up the structural element. In this study, reinforced concrete elements and the redistribution of stress from concrete to reinforcement are considered. To solve the corresponding relaxation problem an approach based on the concept of the strength structure of materials is proposed, which considers them as a union of their fractions (layers, fibers) with statistically distributed strengths. The loss of the ability of force resistance caused by loading by part of the fractions of the element entails a redistribution of stresses to its entire fractions. As a result of this, a nonlinear dependence of deformations on the design stresses arises, calculated under the assumption of equal strength of all fractions. For a material isotropic in strength, the relaxation problem is reduced to solving a linear integral equation conjugated with its linear rheological equation. The linear integral equation relatively structural stresses is reduced. After solving it, the desired stress is determined as the root of the algebraic equation connecting the structural and design stresses. The proposed approach significantly simplifies the obtaining of necessary for the long-term safety prediction of structures stress estimates in the components of structural elements.

The calculation of building structures to a large extent began to be performed using automated software systems based on the finite element method. An urgent issue of the widespread use of this type of calculation is the accuracy of the calculation results in comparison with experimental data. In this study, by numerical simulation using the Abaqus software package, the stress-strain state of a bent reinforced concrete element of a rectangular cross section is investigated. Numerical modeling of the element is performed by volumetric finite elements, taking into account the non-linear (actual) state diagram of concrete, described by the model of plastic fracture of concrete with damage (CDP). Reinforcement is specified by rod finite elements, with a combination of elastic properties and metal plasticity model. The loading of the beam element in the model is performed statically with the application of concentrated forces at the centers of the thirds of the design span. As a result of the finite element calculation, the distribution of stresses in concrete and reinforcement according to Mises, deformations of finite elements along the main axes, as well as a model of concrete damage with increasing load were obtained. The obtained results showed a high convergence with the experimental data of testing beams for bending along a normal section, which allows using this algorithm for automated finite element analysis in the design of bending reinforced concrete structures.

When conducting seismic calculations of reinforced concrete buildings and structures, it is quite important to use nonlinear models of structural performance, including those taking into account the overcritical operation in the fracture stage. The application of such models is especially important if the structures have an initial damage from fire or corrosion, as well as mechanical damage caused by force factors. The purpose of this study is to develop an analytical model of the deformation of eccentrically compressed reinforced concrete columns considering the stage of failure, which includes such processes as spelling of the protective layer, loss of stability of compressed reinforcement, and softening of confined concrete after reaching the design resistance. The existing models describing hysteresis behavior of reinforced concrete structures under low-cycle loading have been reviewed. The models have been analyzed in terms of considering the defining monotone curves, which are the boundaries of cyclic deformation. The model proposed in the research is constructed by analyzing the stages of the stress-strain state of a reinforced concrete column. At each stage, formulas are found for determining moment and curvature by solving equations of equilibrium of internal forces. Calculations based on the obtained model for a particular reinforced concrete column are carried out, monotonous diagrams are obtained, and a conclusion about the significant influence of the level of axial load on the character of deformation is made. On the basis of the obtained model, the construction of hysteresis diagrams under low-cycle loading is expected in the future.