## Vol 16, No 3 (2020)

**Year:**2020**Articles:**9**URL:**http://journals.rudn.ru/structural-mechanics/issue/view/1337**DOI:**https://doi.org/10.22363/1815-5235-2020-16-3

###### Abstract

Relevance. When calculating building structures for dynamic effects, the method of expanding the desired solution in a series according to the forms of natural oscillation is traditionally used. Depending on the complexity of the tasks to be solved, it is required to take into account a different number of forms - from the first few forms to tens or hundreds of forms. The results obtained are all the more accurate the more forms the calculation takes into account. As a rule, the contribution to the required parameters of the stress-strain state of the structure of unaccounted for higher oscillation forms is not evaluated in any way, although in some cases this must be done. In addition, the important question arises of performing the calculation with a reduced number of considered forms so as to obtain a sufficiently accurate result. The aim of the work. This work is devoted to the method of static accounting of higher forms of oscillation in the problems of the dynamics of building structures. The basic principles of the method are described, its use on a spatial rod system loaded with several harmonic forces with different frequencies is considered. Methods. The method of static accounting of higher forms of oscillations studied in this work requires the solution of one dynamic problem with a small number of forms and an auxiliary static problem. An important circumstance of the approach is that the static problem must be solved in two ways: the exact one and the decomposition method according to its own forms of oscillation, after which the static correction to the dynamic solution is calculated. Results . The approach proposed in the article can significantly reduce the computational cost of dynamic calculation in comparison with the classical approach with comparable accuracy of the results. This may be of value in solving problems of complex dynamic effects and for structures with inhomogeneous rigidity.

**Structural Mechanics of Engineering Constructions and Buildings**. 2020;16(3):171-178

###### Abstract

The aim of the work - to propose a scheme and analytical calculation of a statically definable planar truss with a suspended lower belt. Methods. The formula for the dependence of the deflection of the truss under the action of a uniform load on the lower belt on its size and the number of panels is derived in the computer mathematics system Maple. The forces in the rods are found from the solution of the general system of equilibrium equations of all nodes in symbolic form. The deflection is calculated using the Maxwell - Mohr's formula. Generalization of a number of formulas for deflection obtained by increasing the number of panels sequentially to an arbitrary number is performed by double induction using two independent parameters. In this case, special operators of the Maple system are used, allowing for a sequence of coefficients in the desired formula to create and solve recurrent equations that satisfy the elements of the sequences. Results. The obtained solutions have a polynomial form for the number of panels. Curves of deflection dependence on the number of panels are constructed and analyzed. Asymptotic properties of solutions are found in the case of a fixed span length of the structure and a given total load. The proposed scheme is a statically determinate structure with two independent parameters of regularity allows for the finding of a fairly simple analytical solution. The resulting formula is most effective in calculating systems with a large number of elements, where numerical methods tend to accumulate rounding errors.

**Structural Mechanics of Engineering Constructions and Buildings**. 2020;16(3):179-184

###### Abstract

The aim of the work - to analyze the theory, which is widely used in the calculations of various constructions and buildings, consisting of five theories that do not correspond to each other (or erroneous), which reject the fundamental properties of structural concrete and the principles of the Eurocode. Methods. According to the authors and their research this theory contains: a set of theories of various purposes rejecting each other, including erroneous, physically impossible jumps from one theory to another, jumps of various design schemes, unacceptable in the elastoplastic stage. In it: there are mathematical errors; the fundamental concepts of the classical and general theory of calculation are distorted; the principle of designing bearing capacity in ultimate conditions and the process of continuous loading of structures established by the Eurocode are rejected; the fundamental properties in Eurocode of structural concrete are replaced; it is stated that the theory is determined not by the properties of materials, but by the partialities of the developers; references are made to the abstract results of experiments. Results. We analyze the theory of calculating for mass application which accompanied by the necessary mathematical calculations and experimental estimates.

**Structural Mechanics of Engineering Constructions and Buildings**. 2020;16(3):185-192

###### Abstract

Relevance. Due to the widespread use in practice, tubular furnaces were chosen as the object of study of this work. The article provides an analysis of damage to the supporting structures of oil refining tubular furnaces. The causes of damage and the physical nature of the development of damage are established. According to the results of field surveys, it was found that about 10% of the furnaces are operated with damage in the form of significant curvature of the supporting structures that developed as a result of the explosion of the gas-air mixture and the technological product inside the furnace space. The aim of the work is to analyze the damage and assess the impact of damage on the operation of the supporting structures of furnaces. Methods. The main research results were obtained by static numerical analysis of spatial models of furnace frameworks in the LIRA-SAPR software package. This complex belongs to the class of software products that implement the finite element method. Results. According to the results of calculating a series of models of structures, the effect of damage on the operation of the supporting structures of the furnace is determined. Based on the analysis of calculation data for models of tube furnaces with damage and comparison of calculation results for furnace models with structural damage identified during the survey, ways to optimize the design decisions of an industrial furnace are determined. Studies have shown the need to improve the design of tube furnaces in the direction of improving technology and improving the structural form of the supporting frame of the furnace.

**Structural Mechanics of Engineering Constructions and Buildings**. 2020;16(3):193-202

###### Abstract

**Structural Mechanics of Engineering Constructions and Buildings**. 2020;16(3):203-208

###### Abstract

The aim of the work - to research changes in the dynamic stiffness of pile foundations from the distance between the piles during vertical vibrations using experimental data from literature sources and solving wave models describing the vertical vibrations of a thin plate with round cuts. Methods. To verify the reliability of solutions of wave models describing changes in dynamic stiffness during vertical vibrations of pile foundations, it is used data obtained in experiments to determine the eigenfrequencies of 3×3 groups of friction piles with different distances between them. Also the data obtained from forced vertical oscillations of 2×2 groups of friction piles connected by pile-caps at different loads and distances between piles was used. In the processing of available amplitude-frequency curves for determining the dynamic stiffness the inverse problem is solved using the theory of nonlinear oscillations. The correspondence between the measured and predicted data is evaluated, when describing the behavior of the pile-ground system. Results. It is established that the relations that take into account the mutual influence of piles in the group, obtained in the framework of wave models solutions and used for calculating dynamic stiffness in vertical vibrations of pile foundations, allow us to obtain satisfactory results in accuracy. The deviation of the calculation results from the experimental data does not exceed 15%.

**Structural Mechanics of Engineering Constructions and Buildings**. 2020;16(3):209-218

###### Abstract

Relevance. Single-connected and multi-connected plate systems are widely used in construction, aircraft, shipbuilding, mechanical engineering, instrument making. As a result, the study of the stability of geometrically nonlinear plate systems is an urgent topic. But, despite significant achievements in this area, there are still many unsolved problems. Thus, the requests of the above-mentioned areas of application of thin-walled spatial systems require further study of the issue of static and dynamic stability. The aim of the work - development of a method of the dynamic stability analysis of geometrically nonlinear plate systems such as prismatic shells under the action of dynamic compression loads. Methods. A plate system, which is subject to dynamic compression loads in the longitudinal direction, is considered. Kirchhoff - Love hypotheses are taken into account. The material stress-deformation diagram is linear. The displacement of points in the normal direction to the median plane of the plates is determined in the form of the Vlasov expansion. To derive the basic differential equations of stability, the energy method and the variational Vlasov method are used. The extreme value of the total energy is determined using the Euler - Lagrange equation. As a result, a set of basic nonlinear differential equations for studying the buckling of the plate system under the action of dynamic compression loads is obtained. Results. The developed method is used to stability analysis of a geometrically nonlinear prismatic shell with a closed contour of the cross section, under central compression under the action of dynamic loading. The edges of the shell rest on the diaphragm. The buckling of the prismatic shell in the longitudinal direction along one and two half-waves of a sinusoid is studied. The numerical integration of nonlinear differential equations is performed by the Runge - Kutta method. Based on the calculation results, graphs of the dependence of the relative deflection on the dynamic coefficient are constructed. The influence of the rate of change of compression stress, the initial imperfection of the system, and other parameters on the criteria for the dynamic stability of the plate system is investigated.

**Structural Mechanics of Engineering Constructions and Buildings**. 2020;16(3):219-225

###### Abstract

Relevance. Wood is one of the most widely used building materials throughout history, and because of its physical-mechanical properties it mainly has been used in flexed and compressed elements. Eucalyptus was introduced to Latin America in the mid-19th century and nowadays is one of the most used woods for construction in the Andean region of Ecuador. To designing slender structural elements under axial loading engineers usually use the Euler formula, but it is applicable only if the compression stress does not exceed the proportional limit. One way to determine if the compression stress will be below the proportional limit is by comparing of the slenderness of the element with the limiting flexibility of its material which allows knowing if the buckling will occur in the elastic zone where Euler formula applies. The aim of the work - determine the magnitude of the limiting flexibility of eucalyptus, since this wood has been the subject of some investigations, however, no information about the limiting flexibility magnitude for the calculation of axially compressed elements. Methods. The laboratory tests to determine the magnitudes of the modulus of elasticity, proportional limit, admissible compression stress and limiting flexibility was carried out. Results. This experimental investigation shows that the magnitude of the limiting flexibility or so-called critical slenderness ratio for eucalyptus globulus is 59.

**Structural Mechanics of Engineering Constructions and Buildings**. 2020;16(3):226-232

###### Abstract

At present, there is a renewed interest in the design and application of wall structures in architecture and construction. With the advent of modern computers, refined methods for calculating shells, new building materials, the development of differential geometry and the rapid growth of numerical methods of calculation, it became possible to create architectural masterpieces from shells of canonical and non-canonical forms, which can be the hallmark of a city or country. This emerging trend among young Russian and foreign specialists inspires optimism among scientists who are researching thin-walled shells. The article considers some results of the work of the Department of Civil Engineering of the Engineering Academy of the Peoples’ Friendship University of Russia on attracting students to architectural design and involving undergraduates in researches on architecture, the theory of thin-walled spatial structures and their application in construction and architecture. The publications of students in this field are presented.

**Structural Mechanics of Engineering Constructions and Buildings**. 2020;16(3):233-240