"Вестник МГСУ"

In the article the authors describe a method of optimizing the stress state of an elastic beam, subject to the simultaneous action of the central concentrated force and bending moment. The optimization method is based on solving the inverse problem of the strength of materials, consisting in defining the law of changing in elasticity modulus with beam cross-section altitude. With this changing the stress state will be preset. Most problems of the elasticity theory of inhomogeneous bodies are solved in direct formulation, the essence of which is to determine the stress-strain state of a body at the known dependences of the material elastic characteristics from the coordinates. There are also some solutions of the inverse problems of the elasticity theory, in which the dependences of the mechanical characteristics from the coordinates, at which the stress state of a body is preset, are determined. In the paper the authors solve the problem of finding a dependence modulus of elasticity, where the stresses will be constant over the beam’s cross section. We will solve the problem of combined strength (in the case of the central stretching and bending). We will use an iterative method. As the initial solution, we take the solution for a homogeneous material. As the first approximation, we consider the stress state of a beam, when the modulus of elasticity varies linearly. According to the results, it can be stated that three approximations are sufficient in the considered problem. The obtained results allow us to use them in assessing the strength of a beam and its optimization.

In the article the authors propose a simplified method of dynamic analysis of the resistance to progressive collapse of a fragment of the building bearing system with amplified floors. This method is based on representing the building bearing system as a dynamic model with a denumerable number of degrees of freedom, in which the resistance of the system is provided mainly by the behavior of the columns. The degrees of freedom number is determined by the number of floors «hanging» to amplified floors. Thecontribution of slabs in the total system resistance is not taken into account. Stress-strain state of the columns is determined by the non-linear resistance diagram, including three stages: elastic, elastic with cracks and plastic stage connected with plastic yield in the steel of the columns. The criterion of sustainability to the progressive collapse is relative strain of steel of the undestroyed columns. A numerical example of the calculation of the building resistance to progressive collapse in case of sudden destruction of one vertical element based on proposed theoretical method is offered. A model with two numbers of degrees was considered. The suggested method allows estimating the strength, deformability and stability of monolithic reinforced concrete frame buildings with separate amplified floors. In the future it is intended to complicate the model by the accounting for the influence of deformation and constructive solution of the slabs on the stiffness characteristics of the model as a system with a finite number of degrees of freedom.

Basing on the damaging statistics obtained during the on-site inspections of industrial multi-span building structures with under-crane secondary trusses which have continuous lower plinth, we simulated the scenario of the most likely damage development of under-crane secondary trusses.The first scenario is the development of cracks along the total cross section of plinth. In the process of calculations we defined a real deformation scheme of plinth of under-crane secondary trusses with damage and its stress condition.The second scenario is the destruction of a support or support mounting unit to the lower plinth of under-crane secondary trusses. The destruction of this kind can occur as a result of a crack in a support or as a result of destruction of high-strength fasteners of a support to plinth. We discovered that a system with such damage is geometrically unchanged; there is no possibility of sudden destruction of both the under-crane secondary trusses and the entire building frame.The third scenario is the upper plinth separation from one of the walls of lower plinth of under-crane secondary trusses.The scenario is developed to define the viability of under-crane secondary trusses as a result of cracks in the area of wall junction with the upper shelf of lower plinth, their further development and the appearance of discrete cracks developing into a backbone along the entire span length of under-crane secondary trusses.Based on the calculations of the stress strain state of under-crane secondary trusses with damages in the emergency nature in a separate span of the lower plinth and a truss member, we estimated the viability of structure. The analysis of viability limits makes it possible to find the measures of collapse preventing and avoid possible victims.

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.

The present article studies the order of performing low-cycle fatigue strength calculation of the elements of the full-scale specimen construction of the fixed support DN 1000 of the above-ground oil pipeline “Zapolyarye — Purpe” during rig-testing. The calculation is performed with the aim of optimizing the quantity of testing and, accordingly, cost cutting for expensive experiments. The order of performing the calculation consists of two stages. At the first stage the calculation is performed by the finite element method of the full-scale specimen construction’s stressed-deformed state in the calculation complex ANSYS. Thearticle describes the main creation stages of the finite element calculation model for the full-scale specimen in ANSYS. The calculation model is developed in accordance with a three-dimensional model of the full-scale specimen, adapted for rig-testing by cyclic loads. The article provides the description of the full-scale specimen construction of the support and loading modes in rig-testing. Cyclic loads are accepted as calculation ones, which influence the support for the 50 years of the oil pipeline operation and simulate the composite impact in the process of the loads’ operation connected to the changes in the pumping pressure, operational bending moment. They also simulate preloading in the case of sagging of the neighboring free support. For the determination of the unobservable for the diagnostic devices defects impact on the reliability of the fixed support and welding joints of the fixed support with the oil pipeline by analogy with the full-scale specimen, artificial defects were embedded in the calculation model. The defects were performed in the form of cuts of the definite form, located in a special way in the spool and welding joints. At the second stage of calculation for low-cycle fatigue strength, the evaluation of the cyclic strength of the full-scale specimen construction’s elements of the fixed support was performed in accordance with the requirements of Russian State Standard GOST R 52857.6—2007 on the basis of the overall and local stress condition, received according to the results of the calculation in ANSYS. In accordance with the results of the conducted work the conclusion was drawn about fulfilling the standard requirements for the low-cycle fatigue strength of the developed full-scale specimen of the support. Therefore, the application of the modern approaches to the numerical modeling of the fixed support construction operation allowed minimizing the quantity of full-scale tests of the specimen with the cyclic load, escaping the excessive conservatism in evaluation of the cyclic strength and developing of the optimal for the metal intensity construction.

The main object of this study is the reconstruction, renovation and modernization of the housing built in the period 1975—1985. These buildings have low energy efficiency due to the poor thermal insulation properties of the walls. These apartments do not meet the necessary requirements for year round warmth and comfort.Reconstruction is more preferable, than new-build, because of the cost saving for the land acquisition. Reconstruction is generally 1.5 times cheaper than new-build with 25—40 % reduced cost on building materials and engineering infrastructure.Increasing the width of the apartment blocks from 12 to 15 m can save 9—10 % on the consumption of thermal energy for heating and reduce the m2 construction cost by 5.5—7.0 %. In—5-9 storey high-rise buildings the savings are 3—5 %.Therefore, the width of the apartment block should preferably be between 9—12 m but could be extended to 18 m. The depth of the apartments themselves will be 5.4 — 6.0 —7.2 or 9.0 m. During the reconstruction of 5-storey residential buildings (Building Type105) in a seismic zone, an increase in the width of the block and the lateral stiffness of the building is achieved by building a new reinforced concrete (RC) frame on both sides of the building with a depth of between 2 and 6 m. This technique is especially effective in increasing the seismic resistance of the building. Self-supporting walls of cellular concrete blocks (density 600 kg/m3 and a thickness of 300 mm) are constructed on the outside of the frame, taking care to avoid cold bridges.Model studies have shown that in the conditions of hot-arid climate the thickness of the air gap in a ventilated facade does not significantly change the cooling-energy consumption of the building, and heating consumption is significantly increased. The building's energy consumption is most influenced by the volume of the air in the air gap. By increasing the ventilation rate in the air gap, the energy consumption for building heating increases and for cooling — slightly decreases. For the conditions of the northern region of Tajikistan, the recommended optimal thickness of the air gap with ventilation is 60 mm.

This work was carried out to study at the same time the dynamics of wave propagation in plane and axisymmetric plates by finite-difference numerical calculation and by the method of dynamic photoelasticity.In many cases it is possible to carry out the investigation of the dynamic stressed state of solid structures under the impact of seismic waves in plane statement, observing the foundation and the building itself in the conditions of plane deformation. Such problems in structural mechanics are usually investigated on plates providing the conditions of generalized plane stressed condition and accounting for the necessity of the known substitution of elastic constants. In case of applying the model of generalized plane stressed state for investigating two-dimensional waves’ propagation in three-dimensional elastic medium it may be necessary to observe certain additional conditions, which for example limit the class of external impacts of high frequencies (short waves). The use of candling for wave recording in plane models explored with the method of dynamic photoelasticity in the observed cases of impulse loading of the plates with finite thickness gives satisfactory results.

In view of providing durability of constructions, the urgent problem is studying dynamic processes in loaded rod structures occurring in the process of sudden local defects formation, such as breakage of support bonds, partial destruction, transverse and longitudinal cracks etc., which are united under general term "beyond design impacts". To date, a number of problems related to this topic are solved: the problem of dynamic loadings at sudden formation of transverse cracks, the problem of partial tie breaks in the bearings, partial destruction and longitudinal lamination of compound bars. In the paper the authors propose a method of determining the spectrum of natural frequencies of flexural vibrations of a rod system with this type of injury. The results are to be used for modal analysis of forced vibrations of a beam with a defect of longitudinal lamination, depending on its level.

Arch structures of long span buildings’ coverings are more beneficial in respect to material expenses, than beam and frame systems. Constructive schemes of roof frameworks of arch coverings are diverse, which means their operation under loading differs much. The authors offer a number of construction solutions for flat arch coverings of long span buildings. The comparative analysis of these construction solutions is presented. The operation of radial link arch is observed. The arch consists of discontinuous top chord and radial bowstring under the single load (uniformly distributed and concentrated in nods) with different spans and rises. The problem of radial link arch optimization is solved in dependence with arising forces and rise. The optimal camber of arch was found. In further works the authors plan to analyze spans more than 36 meters and solve the problem in case of asymmetrical loadings.

Multilayer exterior walls are wide-spread in modern civil construction. One type of such structures is a three-layer wall with insulation layer made of lightweight concrete and exterior layers made of structural concrete. It is necessary to provide durable monolithic connection of concrete layers in the process of manufacturing this structure in order to decrease the percentage of web reinforcement and increase thermal engineering homogeneity of multilayer exterior walls. Experimental research of three-layer samples with external layers made of claydite-concrete and internal layer made of polystyrene concrete were conducted in order to establish the strength of layer connections in the multilayer exterior wall. Different temporal parameters and concrete strength were assigned during manufacturing of the samples. The samples were tested under axial tension and shear in the layer contact zone. The nature of tensile rupture and shearing failure was checked after the tests. The relations between manufacturing parameters, strength of the concrete used in samples and layer connection strength were established as a result of experimental research. The climatic tests of three-layer exterior wall model made of claydite-concrete and polystyrene concrete were conducted in order to establish the reduction of the layers contact zone strength during the maintenance. The wall model was made of concrete samples of varying strength. The experimental model was exposed to 35 cycles of alternate freezing and thawing in climatic chamber. During freezing and thawing, the strength tests of external and internal layers contact zone by tearing the cylindrical samples were conducted. Consequently, the nature of contact zone strength reduction for the samples with different concrete strength of external and internal layers was established. As a result of the conducted research, the optimal temporal parameters of manufacturing and optimal concrete strength were established. It is recommended to use these parameters in the process of manufacturing multilayer concrete exterior walls in order to provide durability of the concrete layers monolithic connection during maintenance of the structure.

The buildings made of monolithic reinforced concrete currently enjoy great popularity. Along with a great number of advantages of monolithic building, which are repeatedly listed in the works of many authors, there are many unexplored issues which require detailed consideration. The technological concrete joints are among them. The joints are inevitable in the process of construction of almost any monolithic building and their quality affects the reliability of buildings and structures. Despite regular use of the concept of cold joint and clear instructions in building standards on the technology of joint production, most organizations do not follow the correct technology of concreting the elements. As a result, the strength and stiffness characteristics of the construction deteriorate, because the linkage value of new concrete with the old one is significantly lower than in monolith. In order to conduct experimental studies the reinforced concrete beams of rectangular section were produced. As a result of testing, it was determined that the presence of a concrete joint significantly reduces the stiffness and carrying capacity of the structures. It is confirmed by the fact that the received deflections of solid beams without joint are significantly lower than the deflections of beams with cold joint. It also noted that the deflections of the beams manufactured following the normative technology are lower, than the deflections of the beams, manufactured with violation of the rules. Basing on the obtained results, it was concluded, that more detailed study of the work of a construction with cold joints in concrete is required. The reason for it is in the changing for the worse of the strength and stiffness characteristics of structural element, which is made produced with a joint, while in the process of real designing, the monolith buildings are calculated as solid monolithic, without joints.

The steel thin-walled structures are widespread in civil and industrial engineering nowadays. Self-drilling screws or rivets are used to interconnect thin-walled elements. Blind rivets and nuts as connectors are considered in the frames of this paper. Rivets have some benefits over self-drilling screws. They are: we can obtain more dense connection when using rivets. So we can increase bearing capacity of connection; a lower cost of riveted connection; a large variety of installation tools for riveted connection: manual, pneumatic, battery; side; an easy installation: access to the connected element is required only from one. These benefits provide increasingly growling popularity to rivets. In the paper 4 types of rivets are considered: combined (aluminum/steel) blind rivets, zinc-coated steel blind rivets, stainless steel blind rivets and blind nuts. The features of each type of rivets are described in the paper. The influence on the behaviour of connections is revealed. The results of experimental research performed by the authors are presented in the paper. A bearing capacity shear of riveted connections is studied in the experiment. There are 3 types of riveted connections subjected to experiment: connection made by blind combined rivets; connection made by zinc-coated steel blind rivets; connection made by blind nuts. A connection between elements with significantly different thicknesses is modeled in the experiment. In reality this situation takes place, for example, in the roofing of buildings, where trapezoidal sheet can be fastened to purlin by rivets. As a result of the experiment the authors found out that the local deformations occuring under rivet head in the thick element significantly affect the behaviour and bearing capacity of the connection. That’s why the results of connection's bearing capacity obtained in tests were lower than the bearing capacity of rivet declared by manufacturers.

Thin-walled rods are widely used in construction and other industries. In the design of bridges, crane beams, gas-producing constructions there are cases when flange width is greater than the height profile of its wall. The currently used V.Z. Vlasov’s beam approximation in the process of determining the dynamic characteristics, is based on a set of assumptions, which do not allow to take into account the plate properties of thin-walled rods. In this paper the torsional vibrations of thin-walled beams modeled by a system of related plates with different geometrical characteristics are studied using finite element method. Also the case of an asymmetrical I-beam is studied. It was revealed that the transition from the uniaxial system to spatial structure with appropriate geometric parameters of the rod significantly thickens the frequency spectrum and can lead to more complex (mixed) modes of vibration. The author identified the cases when neglect of inertial forces in the wall and flanges and the assumption of non-deformability in the plane of the profile cross-section can lead to errors in determining the frequencies and modes of torsional vibrations. The application limits of the Vlasov’s theory are investigated and practical recommendations are given.

In the article the survey results of durability and crack resistance investigation of masonry are presented. The aim of the investigations is improving calculation methods of masonry and reinforced masonry. The relevancy of the problem is determined by the necessity of new efficient materials implementation. In accordance with scientific search methodology complex investigations were carried out, which includes gathering, analyzing and revising the existing data on the topic together with determining essential factors and their value rate. Within the framework of the investigations the features of masonry have been studied. The developed calculation method on the basis of the theory of resistance of anisotropic materials at the compression, which reflects the stress-strain state features and nature of destruction, allows to carry out an assessment of durability and crack resistance of the compressed members and structures made of masonry. The research results can be used at revising or updating the existing normative documents.

The proposed calculation method is specific in terms of determining the carrying capacity of eccentrically compressed concrete elements, in contrast to the calculation by error method, as in the existing regulations, where in the result of the calculation is not known what is the limit load the eccentric compression element can withstand. The proposed calculation method, the publication of which is expected in the next issue of the "Vestnik MGSU" the above mentioned shortcomings of the existing calculation methods, as well as the shortcomings listed in this article are eliminated, which results in the higher convergence of theoretical and experimental results of eccentrically compressed concrete elements strength and hence a high reliability of their operation.

The present article deals with integrated research works and tests of pipeline supports for the areas of above-ground routing of the pipeline system “Zapolyarye - Pur-pe” which is laid in the eternally frozen grounds. In order to ensure the above-ground routing method for the oil pipeline “Zapolyarye - Pur-pe” and in view of the lack of construction experience in case of above-ground routing of oil pipelines, the leading research institute of JSC “Transneft” - LLC “NII TNN” over the period of August, 2011 - September, 2012 performed a research and development work on the subject “Development and production of pipeline supports and pile foundation test specimens for the areas of above-ground routing of the pipeline system “Zapolyarye - Pur-pe”. In the course of the works, the test specimens of fixed support, linear-sliding and free-sliding pipeline supports DN1000 and DN800 were produced and examined. For ensuring the stable structural reliability of the supports constructions and operational integrity of the pipelines the complex research works and tests were performed: 1. Cyclic tests of structural elements of the fixed support on the test bed of JSC “Diascan” by means of internal pressure and bending moment with the application of specially prepared equipment for defining the pipeline supports strength and durability. 2. Tests of the fixed support under the influence of limit operating loads and by means of internal pressure for confirming the support’s integrity. On the test bed there were simulated all the maximum loads on the support (vertical, longitudinal, side loadings, bending moment including subsidence of the neighboring sliding support) and, simultaneously, internal pressure of the carried medium. 3. Cyclic tests of endurance and stability of the displacements of sliding supports under the influence of limit operating loads for confirming their operation capacity. Relocation of the pipeline on the sliding supports from temperature expansion in case of preheated oil charge into a “cold” pipeline was simulated. 4. Cyclic tests of durability of frictional couples under the influence of operational and maximum loads. On the test bed there were examined various materials for the sliding surface of the supports, ensuring the norm friction coefficient.

The arithmetic model of reinforced concrete slab distortion with a polymer-concrete layer exposed to aggressive influences is introduced. The relevance of this object choice as a matter of actual practice. The least contradictory model for specification of the strain-stress state of reinforced concrete constructions is sampled. The most efficient way of solving such tasks is the finite elements method, which lacks the drawbacks of the finite differences method. In this article, the arithmetic model of hybrid finite element qualification for the armored reinforced concrete slabs design is considered. The problem of reinforced concrete slab with a polymer-concrete layer bending is dealt with in the presence of dynamic deformation and simple loading, which gives the opportunity to introduce concrete as a nonlinear material with its elastic-plastic properties, which stay within the strain potential limits. The deformation of creep is not taken into account. The incremental equations connecting stress and deformation increments are provided.

The superelement of a column of rectangular section made of homogeneous material and intended for linear analysis, developed by authors earlier on the basis of the three-dimensional theory of elasticity, is updated with reference to static analysis of reinforced concrete columns with account for geometrical nonlinearity. In order to get the superelement the column is divided on sections and longwise into eight-node solid finite elements modelling the concrete and two nodes rod elements modelling reinforcement. The elements are connected with one another in the nodes of finite element mesh that provides joint operation of concrete and reinforcement. The internal nodes of the obtained finite element mesh are excluded at the stage of stiffness matrix and load vector of a column calculation. Formulas for calculation of linearized stiffness matrix of a superelement and a vector of the nodal forces statically equivalent to internal stresses are received. The element is adjusted to the computer program PRINS, and can be used for geometrically nonlinear analysis of complex structures containing reinforced concrete columns of rectangular section. Separately standing reinforced concrete column was calculated on longitudinal-transverse bending for the verification of the received superelement. The critical load was determined according to the results of calculation. The determined critical force value corresponds to the theoretical value. Thus, the proposed method of accounting for the geometric nonlinearity in the analysis of reinforced concrete columns can be recommended for practical use.

This paper considers the problem of optimal recovery of bounded analytic functions. Namely, the values of these functions are determined at the point from their values at n given points lying in the unit circle. At first, we recall the necessary basic concepts: error of approximation by some method (which is a complex function of n complex variables), the best approximation method. Some theorems from the works of K.U. Osipenko are discussed: on the existence of a best linear approximation method and on calculating the error of best recovery method. After that we write out the formula for finding the error of best approximation method of bounded analytic functions in a unit circle. The lemma of conformal invariance of optimal recovery problem of these functions follows. We prove that under conformal mapping of the unit circle onto itself the error of the best approximation method before mapping coincides with the error of the best approximation method after mapping. It is also proved that a linear best method after conformal mapping coincides with the linear best restore method before this mapping (wherein the problem of optimal recovery after mapping is considered on the images of n given points lying in the original unit circle). Finally, we consider the problem of optimal recovery of bounded analytic functions in a circle in special case when the given points coincide with the vertices of a regular n-gon, and the point itself coincides with its center (which coincides with the origin). We prove that all the coefficients of the best linear method in this case are identical (wherein we apply the lemma of conformal invariance of optimal recovery problem of bounded analytic functions). The formulas for calculating these coefficients are given (for this purpose we write out an integral). The result is the smart, simple formulas for calculating the coefficients of the best linear approximation method for this particular case.

Thin cylindrical shells are widely used in construction, engineering and other industries. In case of designing a reservoir for the isothermal storage of liquefied gases such cases are inevitable, when housing requires various technical holes. A point wise added mass can appear into practice in the form of suspended spotlights, radar, architectural inclusions in buildings and structures of various purposes. It is known, that the dynamic asymmetry as an initial irregular geometric shape, including holes, and the added mass leads to specific effects in shells. In the paper the impact of a cut on the frequency and form of its own vibrations of thin circular cylindrical shells is theoretically examined with the help of the equations of linear shallow shell theory. For modal equations with Nav’e boundary conditions, we used the Bubnov - Galerkin method. The authors have expressed a formula for finding the lowest of the split-frequency vibrations of a shell with a cutout. It is stated, that in case of an appropriate choice of added mass value the lower frequencies are comparable with the case of vibrations of a shell with a hole. By numerical and experimental modeling and finite element method in the environment of MSC "Nastran" oscillation frequencies a shell supporting a concentrated mass and a shell with a cutout were compared. It is shown, that the results of the dynamic analysis of shells with holes with a suitable choice of the attached mass values are comparable with the results of the analysis of shells carrying a point mass. It was concluded that the edges in the holes, significantly affect the reduction in the lowest frequency, and need to be strengthened.