Vol 14, No 3 (2018)

The paper presents a system of resolving equations describing the stress-strain state of multilayer beams and allowing solving a wide range of problems, such as shear, bending, and normal separation for any number of layers. For each of the layers, hypotheses similar to the Kirchhoff - Love hypotheses are introduced. In the proposed model, the layers interact with a contact layer. The contact layer is an anisotropic medium, which can be considered as a “brush” of elastic short rods. For simplicity, it is assumed that the rods are oriented normally to the contact surface. The use of a contact layer allows such problems as infinite tangential stresses at the interface between the layers near the end of the beam and also to solve the problem of determining the concentration of the shearing stresses occurring at the boundaries between the layers and in the corner points, their variation, for example, in the creep process. The main feature of the proposed model is strict satisfaction of the boundary conditions. In view of the complexity of the resolving system of equations, we consider, as an example, the problem of shearing the layers of a double-layer beam. An analytical solution is obtained that allows qualitative analysis of the influence of mechanical and geometric characteristics on the stress-strain state of the design model, calculate the true adhesive strength, and determine the physical characteristics of the contact layer on the basis of experimental data. A numerical example is given for calculating a beam in two variants of model loading, on the basis of which a relationship was established between the true and average adhesive strength, depending on various parameters.

Stability analysis in civil engineering is traditionally centred on the stability of individual components of a structure, rather than on the stability of the assemblage of structural components. This may be explained by the lack of adequate tools for the stability analysis of complete structures in the past. Recently, the necessity of the development of general rational methods of stability analysis with a model of the complex structure is widely recognized. These methods should reliably predict the overall stability of the structure, the interaction between the components of the structure in providing restraint against instability of individual members, and the local stability of each individual member. Development of such theories and corresponding algorithms require a thorough investigation. The aim of this paper is to investigate the instability of single columns without large deflections by means of the second order structural theory and to study the influence of imperfections on the behaviour of such structural elements.

A method of strengthening reinforced concrete structures by external reinforcement systems based on carbon fiber is widely used. Significant experience is accumulated in industrial and civil construction; there is also a certain experience of strengthening reinforced concrete structures of hydraulic structures. It was necessary to conduct experimental studies to justify technical solutions for strengthening the reinforced concrete structures of hydraulic structures. A characteristic feature of reinforced concrete structures of hydraulic structures is the mandatory availability of inter-block construction joints, which are caused by the need to build massive hydraulic structures with tiers and blocks with interruptions in concreting. Previously studies of reinforced concrete structures strengthened by composite materials were conducted without taking into account the block structure. The results of experimental studies of reinforced concrete beam structures of hydraulic structures reinforced with carbon strips having horizontal and vertical inter-block building seams are presented in the article. Experimental studies of a series of reinforced concrete beam-type models made of concrete of class B15 with longitudinal reinforcement from two bars. Their diameter is 10 mm and class is A500C (percentage of reinforcement 0.39%). The used concrete class is B25 with longitudinal reinforcement of three bars of diameter 12 mm and class A500C (percentage of reinforcement 0.84%). Their inter-block construction joints is before their strengthening and after reinforcement by longitudinal and transverse carbon composite tapes. In this case, a special type of cracking was recorded, in which cracks propagate along vertical and horizontal inter-block building seams. Due to the strengthening of reinforced concrete structures with carbon composite strips, the strength of the structures has increased, on average, by 1.78 times.

This article contains results of experimental research of polytetrafluoroethylene (PTFE) deformation and creep under linear and plane stresses. During the tests predetermined values of real stresses considering current deformation were constant. The equation of mechanical states considering instant elastic, viscoelastic, instant plastic and viscoplastic components of total deformation was obtained. The equation is used for the description of PTFE deformations (F-4, F-4D, F-4D0) under stationary and non-stationary cyclic loads in flat stress condition with an application of material constant volume condition, condition of similarity of deviators of stresses and deformations and with the input of parameters which are functions of the form of stress deviators. The results of PTFE creep investigation under real stresses reaching ultimate values are relevant and unique.

Some results of the complex historical-archival, production-technological and computational-theoretical study of the dome-conical structure of the Kazan circus are presented. The state of structures after 50 years of continuous and troublefree operation is evaluated. Spatial modelling was carried out and numerical verification was carried out using volumetric finite elements (FEM) based on the software package “MiсroFe”. This takes into account: the history of operation of the structure, including the data of engineering and numerical calculations (1976); the features of construction and technology of construction; the results of field tests and physical depreciation of structures. At the first stage, the spatial model of the upper dome structure was calculated, which allowed to estimate and establish the stress-strain state of the frame made of petals-ribs as the left snap of the dome-ribbed coating. In the second stage adopted the estimated spatial scheme with the collaboration of the foundation and superstructure. The calculation takes into account vertical and horizontal loads from all regional climatic influences, as well as technological loads at circus performances. On the basis of complex computational and theoretical studies of stress-strain state dome-conical structure of the building of the Kazan circus, which has the status of a unique object, made conclusions and developed measures to eliminate defects.

In 1938 standards were adopted in which the method of limiting equilibrium, developed by prof. А.А. Gvozdev and V.I. Murashev, was recommended for the calculation of reinforced concrete structures. From the very beginning, the proposed method caused a sharp discussion in the scientific community, since it contained number of contradictions. Most of the contradictions in the theory of A.A. Gvozdev became part of modern Russian standards. Until now the method of limiting equilibrium remains the main method for calculating reinforced concrete structures for strength. In recent years, a discussion has been developed on the transition to the deformation model of reinforced concrete resistance used by the European codes. In view of this, the updated version of domestic regulations allows the calculation of reinforced concrete structures using a nonlinear deformation model. However, there is a limited number of studies confirming the consistency of the proposed deformation model. In this regard we performed a series of calculations of rigidity of hinged supported on the basis of the theoretical and deformation models of the Russian standards. The calculation was carried out by the finite element method using the model of nonlinear deformation of concrete.

In the article are regarded the curves - epiand hypocycloids, which are formed by the moving of the generating points, linked with the circles of the same radius and which are at the same time outside and inside of the unmoving circle. There is shown the relation of those curves. The moving of the circles with constant angle to the plane of the unmoving circle is also regarded. At full rotation of the moving circle the generating point linked with moving circle described a circle around the tangent of the unmoving circle. And the initial point laying in horizontal plane on epicycloid moving to the point on hypocycloid when the moving circle rotates on around the tangent of the unmoving circle. When the circle made a full rotation around the unmoving circle with full rotation around the tangent to the unmoving circle the epi-hypocycloidal cyclic surfaces are formed. In the article is proofed that the circles of the epi-hypocycloidal cyclic surfaces are the coordinate lines of the main curvatures of the surface and so the surfaces belongs to the class of canal surfaces. The drawings of the epi-hypocycloidal canal surfaces with different parameters - relation of the radius of the moving and unmoving circles λ, the position of the generating point μ - are shown.

Design of fiber-reinforced composite of minimum material consumption at guaranteed reliability and durability requires consideration of cases when cracks may appear in the binder. To know the limit bending loads at which cracks will occur in the binder, it is necessary to carry out the limit analysis of the composite. Proposed design model takes into account the presence of damages (zones of weakened inter-particle bonds of the material) in the fiber composite. Based on this design model a calculation method has been developed for composite parameters at which cracks appear. A thin plate of elastic isotropic medium (matrix) and inclusions (fibers) of another elastic material distributed in the matrix is considered. The plate is bending. It is assumed that at the loading of composite, the cracks initiation and fracture of the composite occur. A closed system of nonlinear algebraic equations is constructed. Solution of the obtained system allows to predict the cracking in composite under bending, depending on geometric and mechanical characteristics of the binder and fiber. A criterion of the cracks nucleation in the composite under the action of bending loads is formulated. Size of limit minimal zones of weakened inter-particle bonds of the material at which the cracks nucleation occurs is recommended to be considered as a design characteristic of the binder material.