"Вестник МГСУ"

The article describes the problem of stability of elastic orthotropic rectangular plates for the case when two opposite sides are simply supported, and two other sides have boundary with either simple supports or fixed supports, which are arbitrarily combined. The plate that is simply supported all over the contour is not considered in the article since the authors described it in the earlier publication. The external load is uniformly distributed along the side and is applied to the shorter side of the plate. To solve the stability problem, the authors use an approximate analytical method - the form factor interpolation method, which is based on the functional relationship between an integral geometric parameter of the mid-plane surface (the form factor) and an integral mechanical parameter (the critical force of buckling). Subject: stability of elastic orthotropic rectangular plates for the case when two opposite sides are simply supported and two other sides have combination of simple supports and fixed supports arbitrarily combined. Materials and methods: the form factor interpolation method (FFIM) is used to solve the stability problem of elastic orthotropic rectangular plates. The solutions which were obtained by the FFIM method were compared with the results of calculations by FEM (the program SCAD Office 11.5). Results: for orthotropic rectangular plates with combined boundary conditions, we obtained analytical expressions for critical force surfaces and they depend on an integral geometric parameter - form factor and flexural stiffness ratio. To the authors’ knowledge, these expressions are obtained for the first time. The critical force surface for orthotropic rectangular plates constitutes one of the boundaries of this integral physicomechanical parameter for the entire set of orthotropic plates with arbitrary convex contour. Therefore, this surface can be used for obtaining reference solutions by the form factor interpolation method. We demonstrated how to obtain the solution of the stability problem for orthotropic rectangular plates by the form factor interpolation method using the results obtained from the aforementioned analytical expressions as the reference solutions. The solutions obtained by the form factor interpolation method are compared with the results of calculations by the finite element method and show a good accuracy. Conclusions: the analytical expressions for critical loads presented in this work can be used directly for the stability analysis of orthotropic rectangular plates loaded in one direction as well as to obtain one of the reference solutions by the form factor interpolation method for plates with arbitrary convex contour and combined boundary conditions. The proposed approach can be extended to other forms of plates, boundary conditions and loading types.

Tower cranes are one of the main tools for execution of reloading works during construction. Design of tower cranes is carried out in accordance with RD 22-166-86 “Construction of tower cranes. Rules of analysis”, according to which to ensure stability it is required not to exceed the overturning moment upper limit. The calculation of these moments is carried out with the use of empirical coefficients and quite time-consuming. Moreover, normative methodology only considers the static position of the crane and does not take into account the presence of dynamic transients due to crane functioning (lifting and swinging of the load, boom turning) and the presence of the dynamic external load (e.g. from wind for different orientations of the crane). This paper proposes a method of determining the stability coefficient of the crane based on acting reaction forces at the support points - the points of contact of wheels with the crane rail track, which allows us, at the design stage, to investigate stability of tower crane under variable external loads and operating conditions. Subject: the safety of tower cranes operation with regard to compliance with regulatory requirements of ensuring their stability both at the design stage and at the operational stage. Research objectives: increasing the safety of operation of tower cranes on the basis of improving methodology of their design to ensure static and dynamic stability. Materials and methods: analysis and synthesis of the regulatory framework and modern research works on provision of safe operation of tower cranes, the method of numerical simulation. Results: we proposed the formula for analysis of stability of tower cranes using the resulting reaction forces at the supports of the crane at the point of contact of the wheel with the rail track.

The method of two-sided evaluations is extended to the problems of stability of an elastic non-uniformly compressed rod, the variation formulations of which may be presented in terms of internal bending moments with uniform integral conditions. The problems are considered, in which one rod end is fixed and the other rod end is either restraint or pivoted, or embedded into a support which may be shifted in a transversal direction.For the substantiation of the lower evaluations determination, a sequence of functionals is constructed, the minimum values of which are the lower evaluations for the minimum critical value of the loading parameter of the rod, and the calculation process is reduced to the determination of the maximum eigenvalues of modular matrices. The matrix elements are expressed in terms of integrals of basic functions depending on the type of fixation of the rod ends. The basic functions, with the accuracy up to a linear polynomial, are the same as the bending moments arising with the bifurcation of the equilibrium of a rod with a constant cross-section compressed by longitudinal forces at the rod ends. The calculation of the upper evaluation is reduced to the determination of the maximum eigenvalue of the matrix, which almost coincides with one of the elements of the modular matrices. It is noted that the obtained upper bound evaluation is not worse thanthe evaluation obtained by the Ritz method with the use of the same basic functions.

Application of flexible-walled beams is rather effective because the reducing of wall thickness compared to ordinary welded beams leads to substantial reduction of metal expenditure for the walls and its more rational use. The operation experience of such beams shows that the loss of local stability of a wall takes place near bearing cross section with characteristic diagonal type of half waves, indicating, that the reason for the stability loss is in shear deformation. In plate girder with slender web big transverse forces appear, which leads to its buckling as a result of shear. One of the ways to increase stability of the parts of web near supports is to install stiffeners. In the given work the task of finding critical stresses of fixed square plate with installed inclined stiffener is considered. Investigations were performed with the help of finite element method and were experimentally checked. Recommendations were given on the choice of optimal size of the stiffener.

The problem of stability of polymer rods with account for creeping was resolved using the energy method customized by Tymoshenko and Ritz. Possible patterns of displacements were provided in the form of trigonometric series with undetermined coefficients. The principle of the minimal total potential energy of the system was taken as the basis. According to this principle, the form in which the potential energy has a minimum value is implemented in all possible patterns of deformation occurring due to the loss of stability. The energy method makes it possible to replace the solution of complex differential equations by the solution of simple linear algebraic equations. The result was obtained numerically using MatLab software applicable to different equations describing deformations and stresses caused by the exposure to creeping. The problem was solved for low and high density polyethylene. The equation of Maxwell and Thompson was

The author considers the method of two-sided evaluations in the problems of stability of a one-span elastic non-uniformly compressed rod under various conditions of fixation of its ends.The required minimum critical value of the loading parameter for the rod is the minimum value of the functional equal to the ratio of the norms of Hilbert space elements squared. Using the inequalities following from the problem of the best approximation of a Hilbert space element through the basic functions, it is possible to construct two sequences of functionals, the minimum values of which are the lower evaluations and the upper ones. The basic functions here are the orthonormal forms of the stability loss for a rod with constant cross-section, compressed by longitudinal forces at the ends, which are fixed just so like the ends of the non-uniformly compressed rod.Having used the Riesz theorem about the representation of a bounded linear functional in the Hilbert space, the author obtains the additional functions from the domain of definition of the initial functional, which correspond to the basic functions. Using these additional functions, the calculation of the lower bounds is reduced to the determination of the maximum eigenvalues of the matrices represented in the form of second order modular matrices with the elements expressed in the form of integrals of basic and additional functions. The calculation of the upper bound value is reduced to the determination of the maximum eigenvalue of the matrix, which almost coincides with one of the modular matrices. It is noted that the obtained upper bound evaluations are not worse than the evaluations obtained through the Ritz method with the use of the same basic functions.

Differential equations of motion for a bar are provided in this paper. The bar is exposed to the applied force that intensifies as the time progresses. The condition substantiating the trans-versal inertia force is identified using the equations. On top of the emerging inertia force, brief high-speed stress increases the yield stress of the material.The external force is accompanied by the eccentricity. Therefore, linear dimensions of the bar and its eccentricity make plastic behaviour possible both in compressed and stretched areas of the rod sections. Patterns of distribution of plastic deformations (one-sided and double-sided yield) are generated using the equations of motion for each case. Cauchy problems are supple- mented by the incoming conditions according to the principle of continuity of displacement and velocity.The criterion of stability loss is a condition when the variation of the exterior torque equals to the variation of the interior torque. At the same time, the variation of a longitudinal force must be equal to zero. Having completed a series of transformations, the author obtains the stability loss functional. It is calculated simultaneously with the motion equation. When the functional is equal to zero, the bearing capacity is exhausted.Moreover, there is a simplified method of identifying the critical force. The comparison of values with the testing findings demonstrates the efficiency of employment of the approximate method.

The authors present both top and bottom limit values of loads within the two problems of stability of a rectilinear elastic cantilever bar that has a variable cross-section. In the first problem, a longitudinal compressive force applied to the bar end is transmitted through a connecting rod that has hinges on both ends, while the second problem is to be resolved in absence of any connecting rod.
The authors apply well-known expressions to identify the stability loss by a rectilinear elastic cantilever bar that has a constant cross-section compressed by a longitudinal force at its free end, with account for the inequalities generated by the best approximation problem in the Hilbert space. They constructed two series of functionals, the bottom bounds of which are the bilateral bounds of the unknown critical value of the load parameter. The calculation of the bottom bounds is reduced to determination of the biggest eigenvalues for the matrices presented in the form of second-order matrices with elements, expressed through the integrals of well-known forms of stability loss by a bar that has a constant cross-section. The calculation of the top bound is reduced to the determination of the biggest eigenvalue for the matrix which almost coincides with the one of the block matrices constructed for the determination of the bottom bound.
Bilateral bounds identified in accordance with the above method make it possible to assess the reduction of the critical load value in the first problem and to compare it to the one of the second problem.

The given paper is devoted to strength and stability analysis of load-bearing structures of a high-rise (54-storey) building with allowance for actual positions of reinforced concrete structural members (columns and walls). Finite element method (FEM) is used for structural analysis. The authors present formulations of problems, governing equations, information about basic three-dimensional finite element models (so-called “design” (ideal) model, the first “actual” model (taking into account the deviations of positions of columns from the project) and the second “actual” model (taking into account the deviations of positions of walls from the project)) of the coupled system “high-rise building - foundation” within ANSYS Mechanical software and their verification, numerical approach to structural analysis and corresponding solvers. Finite element models include mainly 4-node structural shell elements (suitable for analyzing foundation slabs, floor slabs and load-bearing walls) and three-dimensional 2-node beam elements (suitable for analyzing beams and columns), special spring-damper elements and multipoint constraint elements. Detailed finite element mesh on the bottom foundation slab is agreed with the location of piles. The advanced model of Prof. Yu.K. Zaretsky is used for approximation of soil behavior. Construction sequence and various types of nonlinearities are taken into account. The results of modal analysis, static and dynamic analysis with various load combinations (gravity load, facade load, dead (constant) loads, temporary loads, wind load, snow load, crown load etc.) are considered, the results of the regulatory assessment of the strength of structures (obtained with the use of corresponding software in accordance with design codes of the Russian Federation) are under consideration as well. The corresponding displacements, stresses, natural vibration frequencies can be used for research and development of the correct monitoring method of the foundation and load-bearing structures of a high-rise building.

The problem connected with the stability of compressed-bendable rigid rods of variable rigidity (with the reduced rigidity in the centre) is formulated and solved. The system of transcendent equations with roots for critical load for a rod is founded out.

In the modern construction, shipbuilding, mechanical, aircraft engineering and other fields of industry structures in the form of shells, including orthotropic shells, gained widespread currency. In order to raise their rigidity they are strengthened by reinforcing elements (ribs). In the process of shell constructions’ design the choice of rational construction parameters is very important (rational placement of ribs, their rigidity, curvature). The volume of the shell material is usually a minimalised efficiency function. At that the limit values of stress level in the shell and its stability are the restrictions. It is proposed to use variation and parametric method for choosing the angle and reinforcements by stiffening plates so that the shell construction would not lose its stability and reliability. The applied method with change of continuation parameters gives a scheme of coordinate-wise incline, which provides relative simplicity of choosing rational construction type in case of the given loads and restrictions on its stress-strain state.

The author considers the method of two-sided evaluations in solving the problems of stability of one-span elastic non-uniformly compressed rod with variable longitudinal bending rigidity in case of different classic conditions of fixation of the rod ends. The minimum critical value of the loading parameter for the rod is represented as a problem of calculating minimum value of the functional corresponding to the Euler equation, which is the same as the integral equation for the rod stability. Using the inequalities following from the problem of the best approximation of a Hilbert space element through the basic functions, the author constructs two sequences of functionals, the minimum values of which are the lower evaluations and the upper ones for the required value of the loading parameter. The basic functions here are the derivative forms of the stability loss for a rod with constant cross-section, compressed by longitudinal forces applied at the rod ends. The calculation of the lower bounds value is reduced to the determination of the maximum eigenvalues of block matrices. The elements of the aforesaid matrices are expressed through the integrals of basic functions depending on the type of the fixation of the rod ends. The calculation of the upper bound value is reduced to the determination of the maximum eigenvalue of the matrix, which almost coincides with one of the modular matrices. It is noted that the obtained upper bound evaluations are not worse than the evaluations obtained by the Ritz method with the use of the same basic functions.

The underground space is widely used in the construction in big cities of the Russian Federation. These works need the use of elevating-transfer vehicles. In this case the requirements of norms and regulations on operating safety should be strictly observed, because their breach often leads to emergency situations and injuries. The organizational and technological solutions when developing the design documentation and executing construction and assembly works should be primarily based on the stability of lifting facilities. The author states the requirements to installation of lifting tackles (cranes). The features of their installation in different operation conditions on construction sites are described. The crane stability depends on many different indicators, which are considered by the author. The calculation algorithms of crane stability are offered.

Dry construction mixes are today a product of high technologies. Depending on the purpose and requirements to the properties it is easy to produce dry construction mixes with different compositions and operating indicators in plant conditions using the necessary modifying additives. Cement, gypsum and other mineral binders are used in the construction mixes. Different types of cement are more heavily used in dry construction mixes. Such dry mixes are believed to be more effective materials comparing to traditional cement-sandy solutions of centralized preparation. The authors present the results of the investigations on obtaining biocidal cement-sand compositions. It was established, that introduction of sodium sulfate into the composition provides obtaining the materials with funginert and fungicide properties. The strength properties of the mixes modified by carbon nanotubes and biocide additive were investigated by mathematical planning methods. The results of the investigations showed that the modification of cement stone structure by carbon nanotubes positively influences their strength and technological properties. Nanomodifying of construction composites by introducing carbon nanotubes may be effectively used at different stages of structure formation of a construction material.

In the article the authors estimate the possibility of building a high (100 m high) stone dam with clay-cement concrete diaphragm. This diaphragm is used as an antifiltering element and it is made of secant piles method of clay-cement concrete (method of "slurry wall"). This diaphragm should be constructed in several phases, in our example example in three stages. Numerical studies of the stress-strain state of such a dam show that considerable compressive stresses can appear in the diaphragm. These stresses can be significantly (3...4 times) greater than the strength of clay-cement concrete in compression. However it should be taken into consideration that the diaphragm of such a high dam will be crimped by horizontal stresses, i.e. clay-cement concrete will operate in the triaxial compression. Under these conditions the strength of clay-cement concrete will be significantly higher, therefore, the diaphragm reliability might be provided with a margin. For this reason, the most important issue in the engineering of a high dam with such type of diaphragm is to select the required composition of clay-cement concrete. Increasing its strength by extension of the cement fraction could increase modulus of deformation. Therefore it could lead to compressive stress increase and the strength state degradation. Hydrostatic pressure generates the areas of tensile stresses in the clay-cement concrete diaphragm due to the arising bending deformation. It threatens the formation of cracks in the clay-cement concrete, especially in the nodes interface diaphragm queues. It is recommended to match the diaphragm queues using ferroconcrete galleries. This should ensure flexibility of deformation between the gallery and the diaphragm.

In the article, the author proves that the resistance to crises that originate both inside the organization
and in the external environment has a great importance in terms of formation of stability
of the organizational structure. In this article, the issue of flexibility of the organizational structure is
considered; the author demonstrates that the rapidity of the system response to any internal and
external impacts is essential for the purpose of appraisal of the system properties. The analysis
performed by the author serves as the basis for his recommendations designated to assure the
organizational stability in the course of any potential crises.

In the article, the author proposes an original method of identification of upper and lower bounds of critical values of loading parameters in respect of three stability problems for a non-uniformly compressed rectilinear one-span elastic rod with a varying longitudinal bending stiffness value.Initial variational formulations of stability problems under consideration are presented through internal bending moments that emerge at the moment of the rod stability loss and that satisfy uniform boundary conditions rather than additional integral conditions. The author has obtained forms of the bending moment and respective loading parameter values in case of the rod equilibrium bifurcation in the basic problem of stability of an elastic rectilinear rod with a constant cross section, compressed by longitudinal forces at the rod ends.The calculation of the lower bound is reduced to determination of the greatest eigenvalues for the matrices presented in the form of modular matrices of the second order with the elements expressed through the integrals of available forms of bending moments. The calculation of the upper bound is reduced to determination of the greatest eigenvalue for the matrix that almost coincides with one of modular matrices.

Discrete properties of substances found in the water can provide exhaustive information about the substances contained in it. However, they do not provide any information about the interaction between the substances and the water, or between themselves, or the overall properties of the aquatic system. Therefore, they cannot serve as the basis for the systemic approach to development of efficient water treatment technologies.
The author's suggestion is to introduce the term "aquatic system" as a description of the properties of natural and sewerage water. An aquatic system represents a collection of interconnected substances and phenomena in the aquatic medium. Therefore, natural and sewerage water represent aquatic systems, or mixtures of substances that have different origins, that interact with one another on a non-stop basis, and that are interrelated, and that interact with the water at one and the same time. Primary features of aquatic systems are considered in the article, including genesis, stability, and localization. Secondary features of aquatic systems, including their aggregate state, their biotic state, and their chemical composition.
The research of aquatic systems of natural and sewerage waters, their structure and interrelations identifies the top-priority subject of research in the aquatic ecology. Therefore, the subject matter of the aquatic ecology represents the area of research, learning and systematization of features and properties of natural and man-made aquatic systems. This area of research dives way to a new trend of the methodology of modeling and optimization of natural and sewerage water treatment technologies. Aquatic ecology is to develop the principal provisions aimed at the improvement of water treatment technologies based on the properties of aquatic systems.

The author considers the variational formulations of the problem of stability of non-uniformly
compressed rectilinear elastic bars that demonstrate their variable longitudinal bending rigidity in the
event of different classical conditions of fixation of bar ends.
Identification of the critical bar loading value is presented as a minimax problem with respect
to the loading parameter and to the transversal displacement of the bar axis accompanied by the
loss of stability. The author demonstrates that the critical value of the loading parameter may be formulated
as a solution to the dual minimax problem. Further, the minimax formulation is transformed
into the problem of identification of eigenvalues in the bilinear symmetric and continuous form, which
is equivalent to the identification of eigenvalues of a strictly positive, linear and completely continuous
operator. The operator kernel is presented in the form of symmetrization of the non-symmetric
kernel derived in an explicit form.
Within the framework of the problem considered by the author, the bar ends are fixed as follows:
(1) both ends are rigidly fixed, (2) one end is rigidly fixed, while the other one is pinned, (3) one
end is rigidly fixed, while the other one is attached to the support displaceable in the transverse direction,
(4) one end is rigidly fixed, while the other one is free, (5) one end is pinned, while the other
one is attached to the support displaceable in the transverse direction, (6) both ends are pinned.

The problem of stability of a freely supported truncated circular conical shell, compressed by the upper base of a uniformly distributed load per unit length , referred to the median shell surface and directed along the generatrix of the cone, was solved by the Ritz-Timoshenko energy method. The orthogonal system of curvilinear coordinates of the points of the middle surface of the shell was adopted to solve the problem. Possible displacements were selected in the form of double series approximation functions. The physical principle of inextensible generatrix of the cone exposed to buckling at the moment of instability was employed. In addition, the fundamental principle of continuum mechanics, or the principle of minimal total potential energy of the system, was taken as the basis. According to the linear elasticity theory, energy methods make it possible to replace the solution of complex differential equations by the solution of simple linear algebraic equations. As a result, the problem is reduced to the problem of identifying the eigenvalues in the algebraic theory of matrices. The numerical value of the critical load was derived through the employment of the software.