Flat bending stability problem of constant rectangular transverse section wooden beam, loaded by a concentrated force in the middle of the span is considered. Differential equation is provided for the cases when force is located not in the center of gravity. The solution of the equation is generated numerically by the method of finite differences. For the case of applying a load at the center of gravity, the problem reduces to a generalized secular equation. In other cases, the iterative algorithm developed by the authors is implemented, in the package Matlab. A relationship is obtained between the value of the critical force and the position of the load application point. For this dependence, a linear approximating function is chosen. A comparison of the results obtained by the authors with an analytical solution using the Bessel functions is performed.

Keywords: flat bending stability, secular equation, finite difference method, iteration process

This article identifies the problem of a modern heating system, which consists in the drop in pressure at specific sites, which lead to a decrease in thermal performance. For practical research, a scheme has been developed whose purpose is to determine the hydraulic losses in 2 sections, with reinforcement mounted on them, which have a certain coefficient of resistance. The basis for the calculation is the method of specific pressure loss.

Keywords: hydraulic resistance, heating system, pressure loss, local resistance

The article is devoted to the reduction of steel consumption in the compressed zone of reinforced concrete elements. Special attention is paid to the combined prestressing, in which the armature of the stretched zone is subjected to prestressing, and compressed – prestressing. The combined prestressing allows to reduce the steel consumption, and also to increase the performance of many technical characteristics by increasing the limit stresses in the high-strength reinforcement of the compressed and stretched zones

Keywords: the combined prestressing, compressed area, consumption of steel compressed fittings

The article deals with the mechanical and mathematical model of deformation and development of zones of plastic deformations in landslide slopes under static and dynamic influence taking into account physical and geometrical nonlinearity.

Keywords: landslide slope, plastic deformation zone, dynamic impact, physical nonlinearity, geometric nonlinearity, stress deviator, stress tensor, deformation of the soil medium

It was considered the method of calculating the stability of steel spiral-bound silo wall under axisymmetric buckling under the influence of internal grain pressure is considered. The silo construction consists of short, cylindrical shells smoothed through the folds and having initial curvatures directed inwards. It was obtained the solution for determining the critical stresses of short shells.

Keywords: steel silo, spiral-bound silo wall, ax symmetric buckling, initial curvature of the shell, internal lateral pressure, elastic repelling of grain, frictional force of grain

The paper proposes a description of the developed optical measuring set-up for the contactless recording and processing of measurement results for small spatial (linear and angular) displacements of control surfaces based on the use of laser technologies and optical interference methods. The proposed set-up is designed to solve all the arising measurement tasks in the study of the physical and mechanical properties of new materials and in the process of diagnosing the state of structural materials by acoustic active methods of nondestructive testing. The structure of the set-up, its constituent parts are described, and the features of construction and functioning during measurements are discussed. New technical solutions for the implementation of the components of the set-up under consideration are obtained. The proposed set-up is intended for use in instrumentation, mechanical engineering, shipbuilding, aviation, energy sector, etc.

Keywords: optical measuring complex, non-contact measurements, measurements of small spatial displacements, structural materials, diagnostics of the state

The deformation model is considered in relation to the bending elements most characteristic of partially prestressed reinforced concrete structures. The bearing capacity and deformability of partially prestressed structures are investigated. Given the criteria of strength of compressed concrete that meets the attainment of the ultimate strain in the compressed concrete, as well as stretched in the longitudinal reinforcement, characterized by the achievement of the ultimate strain either in stressed or non-stressed reinforcement. The analysis of the calculation results of the strength and deformability of partially prestressed structures under short-term and long-term effects of the load on the deformation model and the norms. It is shown that the deformation model accurately estimates partially prestressed reinforced concrete elements with different types of loading for any combination of tensioned and non-tensioned reinforcement by strength and deformation.

Keywords: partially prestressed elements, deformability, strength, non-stressed reinforcement, state diagrams, deformation model

The effect of auto-displacement in a resonant-tunnel diode (RTD) on the dynamic range of amplifiers on these diodes is considered. Taking into account autosplacement, two possible types of amplitude characteristics and boundaries of their existence were revealed. For these two types of amplitude characteristics, expressions were obtained that determine the dynamic range of the amplifier. When using the amplitude characteristic of the first type, the auto-shift expands the region of existence of this amplitude characteristic and leads to a decrease in the dynamic range. For amplitude characteristics of the second type, a certain expansion of the dynamic range can be achieved.

Keywords: a resonance-tunnel diode, a current-voltage characteristic of a diode, a dynamic range, a gain factor, the degree of regeneration, and the power supply mode of an amplifier for an RTD.

In this paper we consider the bending of a plate on an elastic base. Plate in plan has a rectangular outline. The plate material is isotropic. The plate is supported by ribs of rigidity directed parallel to the sides of the plate. It is taken into account that ry-bra, rigidities parallel to different sides, have different rigidity for bending and torsion. The calculation scheme assumes an orthotropic plate having various cylindrical stiffnesses in two mutually perpendicular directions parallel to the reinforcing ribs. The elastic foundation is adopted by Winkler, ie. it is believed that the reaction of the base is directly proportional to the deflection of the plate at each point. The plate rests on an elastic base and is loaded with a distributed load according to the following law q=q_0*sin⁡〖2πx/a*cos⁡〖πy/2b〗 〗. The problem is solved by the inverse method. Function of deflections of the plate are: w=C*sin⁡〖2πx/a*cos⁡〖πy/2b〗 〗.The stress state is studied and the load-carrying capacity is calculated for various parameters of the plate and the base.

Keywords: ribs, plate, elastic base, inverse method, thin, orthonormal, bending, load-carrying capacity, strength

It was considered the method of calculating the stability of steel spiral-bound silo wall under axisymmetric buckling under the influence of internal grain pressure is considered. The silo construction consists of short, cylindrical shells smoothed through the folds and having initial curvatures directed outwards. It was obtained the solution for determining the critical stresses of short shells.

Keywords: steel silo, spiral-bound silo wall, ax symmetric buckling, initial curvature of the shell, internal lateral pressure, elastic repelling of grain, frictional force of grain

In the paper, a rectangular plate, reinforced by ribs in two mutually perpendicular directions. The plate rests on an elastic Foundation and loaded by a distributed load following the law q=q_0*sin⁡〖2πx/a*cos⁡〖πy/2b〗 〗. The problem is solved by the inverse method. Function of deflections of the plate are: w=C*sin⁡〖2πx/a*cos⁡〖πy/2b〗 〗.The settlement scheme was adopted of simply supported orthotropic plate on an elastic Winklevosses basis. Examines the stress state and calculation of carrying capacity for different parameters and base plates. The calculations showed that the capacity of the wavy plate is higher compared with the load capacity of the flat plate.

Keywords: diversification of management, production diversification, financial and economic purposes of a diversification, technological purposes of ensuring flexibility of production

Now elements of natural structures of the world surrounding us form a basis for loan by their architects and designers in their professional activity. It is caused not only by esthetic appeal of natural objects, but also big functionality of their form providing high degree of durability, reliability, adaptation to the changing external conditions, comforts of their use as inhabited and production rooms. In this work the analysis of the VAT of an oviform envelope under the influence of sole weight and intrinsic pressure is provided.

Keywords: intense strained state, finite element method, oviform envelope, sole weight, intrinsic pressure, analysis, efforts, deformation

The non-continuous beam on which the concentrated masses are located on the elastic supports is subjected to seismic action as a stationary random process with latent periodicity. The eigenfrequencies of the oscillations are determined and the reliability function is found in time. The theory of emissions beyond the design resistance is used.

Keywords: Beam, concentrated mass, elastic support, correlation matrix, natural frequency, effective frequency, random process, latent periodicity, reliability, time

Technical and economic indicators of different options of structural solutions of overlappings are compared. According to the results of the calculations, the most economic profitable option is determined.

Keywords: floor, reinforced concrete, ribbed, monolithic, precast, hollow, profiled, flooring, steel concrete, consumption, reinforcement, concrete, labor input

The article deals with creep in structural mechanics. Systems of non-linear resolving equations for different types of creep kernels are written. An algorithm for solving the problem of nonlinear heredity is considered.

Keywords: creep, nonlinear heredity, creep kernel approximations, finite elements method, exponential-type kernels, least-squares method, collocation nodes

The article deals with the method of probability calculation for seismic stability with the use of stochastic linear equation, the solution of which is carried out by the method of canonical expansion. The obtained expressions for the spectral output density and dynamic coefficient are given.

Keywords: probability calculation, the method of canonical expansions, seismicity, dynamic factor, stochastic equation

This article describes the definition of the approximating function of deflections of building structures using the method of least squares.

Keywords: the approximation function, the least squares method, the deflections of structures, prediction of deformations, the deformation of the structures

The article deals with the issues of impact interaction of particles with layers of dispersed material of different thickness. The influence of the interaction velocity and the thickness of the substrate on the appearance and structure of the collision result is investigated. It is established that at low speeds there is a crater formation while the particle is on the substrate surface. With the growth of the interaction rate, the formation of a crown is observed, and particles penetrate into the substrate material. Experimentally determined the values of the velocity and thickness of the substrate, corresponding to the beginning of the formation of the crown.

Keywords: particle, blow, flow, splash, reflection, speed, stream, the bulk material flow, the recovery factor of speed, the substrate

The article presents the results of experimental studies of alternating torsion under a rigid loading regime, during which the features of the behavior of materials under such loading are revealed. The study of deformation diagrams in the sequence of load cycles and under loading with a stochastic sequence of intermediate unloadings of the sample is carried out. In this case, external force and deformation were measured, followed by recalculation into tangential stresses and the relative twist angle. It is established that the hysteresis loop of the first loading cycle differs considerably in shape from the subsequent cycles, but after three or four loads, the dimensions and shape of the loop in all cases stabilize. When loaded with intermediate discharges, small random loops do not go beyond the main (limiting) hysteresis loop, but are inside it, and the inner and outer branches are similar curves

Keywords: torsion, deformable in the elastoplastic region, rigid loading regime, pattern deformation pattern, loading cycle, energy absorbing element, hysteresis loop

Investigation of the stability of rectilinear rods, determination of critical loads, determination of eigenvalues ​​and forms using numerical methods and modern software.

Keywords: The stability, critical force, differential equations, square matrix, distributed load, rod of variable cross-section, bending moment, lateral force, moment of inertia

The problem of formalizing the elastic line of a thin steel strip of great flexibility arose in the process of creating elastic elements with a nonlinear characteristic for use in various kinds of damping devices. Such elastic rods experience large displacements when the material operates within the elastic range, in particular when axial loading in the supercritical region, when the axial load exceeds the Euler force, but in the subcritical region the movements are not significant enough to obtain a regressive-progressive characteristic.The paper investigates the possibilities of softening the elastic characteristics under axial loading in the initial period by applying a rigid cantilever arm mounted on the end of the elastic rod with a vertical load applied to it. Simultaneously, the influence of the vertical force on the elastic characteristic of the circular trajectory is investigated. To formalize the stress-strain state of a thin steel plate of great flexibility, the method of elliptic parameters is applied. The resulting elastic characteristic actually has a regressive-progressive character. The results obtained using the ANSYS computation complex for a system with given geometric parameters correlate quite well with the theoretical dependences derived. It follows from the diagram that the eccentric compression of the elastic element forms a regressive part of the elastic characteristic, and the circular trajectory of the point of application of the vertical force forms a progressive section.

Keywords: elastic line, thin strip, greater flexibility, formalization, off-axis loading, elliptical parameters, regressive-progressive characteristic

The lack of standards for the calculation of lightweight thin-walled steel structures allowed low-quality producers to save on production, which endangered the people who exploited such buildings. The appearance of normative documents for the calculation of thin-walled structures entails responsibility for the affirmers of these normative documents. In Russia, such norms appeared relatively recently and the purpose of this study was to compare domestic normative methods of calculation with non-significant ones. During the presentation of the study, the concept of a reduced (effective) section of a beam when working on bending was considered. Also, the same stages of the calculation methods were noted, indicating the places where the methods differ in their opinions. The result of this study is a comparison table for the basic geometric characteristic for obtaining the bearing capacity of an effective torque element of resistance. An analysis was carried out and a conclusion was drawn on these values.

Keywords: steel structures, light steel thin-walled structures, thin-walled beams, reduced cross-section, bending work, C-shaped profile, effective cross-section, effective area, effective resistance moment

In this paper, it is proposed to update the values ​​of the bearing capacity of the hinge attachment of the beams to the columns on 2 bolts. A comparative analysis of the bearing capacity of the assembly presented in the 2.440-2 release 1 series and calculated according to modern building codes is carried out. Five calculation formulas were obtained for the five possible limiting states of the node. A table with the values ​​of the limiting forces perceived by the connection is presented. A possible variant of improving the assembly is presented, by including a support table in the work.

Keywords: bearing capacity, metal structures, hinged unit, structural solution, connection of elements, limit state

The analysis of publications and the results obtained in the field of dynamic behavior of inhomogeneous beams and rods based on foreign press materials is performed. The work consists of an introduction and six sections. The introduction discusses the relevance of the problems associated with the study of inhomogeneous beam vibrations. The second part is devoted to highlighting the achievements in the development and application of analytical methods. The next paragraph deals with various aspects, reflecting the variety of dynamic phenomena arising in geometrically heterogeneous beam structures. Results related to modeling of conical, stepped beams and rods having different types of geometric features are discussed. The fourth section considers the state of the art for dynamic problems for physically inhomogeneous beams. It is shown that structural heterogeneity can be associated not only with material properties, but also arise due to external influences, such as inertial and temperature loads. Considerable attention is paid to questions related to the effective use of structurally heterogeneous beams in the field of architecture, construction, robotics, aeronautics and other innovative fields. The sixth and seventh paragraphs give an overview of the existing numerical approaches for an approximate and reliable description of the dynamic processes taking place in inhomogeneous beams. Different industrial software packages are discussed that allow solving dynamical problems of beams with varying physical and geometric properties within a reasonable time and with a high degree of accuracy. In the seventh, the final part, much attention is paid to the application of the finite element method.

Keywords: dynamics, a beam with a variable cross-section, eigenvibrations, numerical methods, structural inhomogeneity, finite element method, functionally graded materials

The article describes the basic concepts of the three-dimensional analogue of Mandelbrot set and fractal architecture. The ideas of fractal structure shaping in the process of parametric and fractal design are outlined. The algorithm for fractals visualizing in geometric forms is proposed, implemented in the program "3D fractal modeling", developed by the authors. The complex fractal structure of the three-dimensional Mandelbrot fractal is examined layer by layer and compared with the Buddhist mandalas and the architecture of the pagodas.

Keywords: fractal, fractal geometry, Mandelbrot set, volumetric fractal , three-dimensional Mandelbrot fractal modeling, fractal structure,