## Vol 17, No 2 (2021)

Analysis and design of building structures
The method of compensating loads for solving of problems of cyclic symmetrical flexure of anisotropic plates, resting on an elastic subgrade
Koreneva E.B.
###### Abstract

The purpose of the study - receiving of exact analytical solutions of statics problems of anisotropic plates, resting on an elastic subgrade and subjected to an action of cyclic symmetrical loads. The method of compensating loads is used for solving of the formulated problems. The basic and the compensating solutions are determined. The new approach, connected with the use of Nielsen’s equation for receiving of the solutions, is applied. For the first time by means of the method of compensating loads the exact analytical solutions of the cycle symmetric flexure of anisotropic circular plates, resting on the elastic subgrade, are received. Various boundary conditions and the loads, distributed along circumferences and over ring surfaces, are considered. The problem of anisotropic infinite plate with the circular opening, resting on the elastic subgrade, is also examined. All the solutions are obtained in the closed form and expressed in terms of Bessel functions.

Structural Mechanics of Engineering Constructions and Buildings. 2021;17(2):99-111
Mathematical modeling of stress waves under concentrated vertical action in the form of a triangular pulse: Lamb’s problem
Musayev V.K.
###### Abstract

The aim of the work. The problem of numerical simulation of longitudinal, transverse and surface waves on the free surface of an elastic half-plane is considered. Methods. To solve the non-stationary dynamic problem of elasticity theory with initial and boundary conditions, the finite element method in displacements was used. Using the finite element method in displacements, a linear problem with initial and boundary conditions was led to a linear Cauchy problem. A quasiregular approach to solving a system of second-order linear ordinary differential equations in displacements with initial conditions and to approximating the area under study is proposed. The method is based on the schemes: point, line and plane. The study area is divided by spatial variables into triangular and rectangular finite elements of the first order. According to the time variable, the study area is divided into linear end elements with two nodal points. The Fortran-90 algorithmic language was used in the development of the software package. Results. Some information is given about numerical modeling of elastic stress waves in an elastic half-plane with a concentrated wave action in the form of a Delta function. The estimated area under study has 12 008 001 nodal points. A system of equations consisting of 48 032 004 unknowns is solved. The change of elastic contour stress on the free surface of the half-plane at different points is shown. The amplitude of Rayleigh surface waves is significantly greater than the amplitudes of longitudinal, transverse, and other waves with a concentrated vertical action in the form of a triangular pulse on the surface of an elastic half-plane. After surface Rayleigh waves, a dynamic process is observed in the form of standing waves.

Structural Mechanics of Engineering Constructions and Buildings. 2021;17(2):112-120
Joint operation of the cellular structure as a system “frame - filling ground - base”
Zimnyukov V.A., Zborovskaya M.I.
###### Abstract

Relevance. The experience of constructed cellular structures and the results of computational and model studies carried out in our country and abroad to assess the joint work of the complicated complex “cellular frame - soil backfill of cells - foundation” indicates the sufficient reliability of such hydraulic structures. The main difficulty in the design of cellular structures is to reproduce the volumetric work of the complex “cellular frame - backfill soil - foundation soil” to identify structural reserves. Objectives. To study, through laboratory studies, the interaction of the frame and backfill of the cell and the base at different soil moisture, taking into account such factors as the granulometric composition of the backfill soil, the role of the surface tension of moisture contained in the soil, the geometric parameters of the structure itself and a number of other factors. Methods. Experimental studies on the model of the operation of a cellular structure without a bottom on a non-rocky (sandy) foundation for stability, subject to the similarity criteria, as well as studies of cells with different geometry and sizes with changes in moisture and particle size distribution of the soil of the cells. Results. Based on the results of model studies, a dependence is proposed to take into account the effect of surface tension forces, considering the hydraulic radius of the cell cross-section, wetted perimeter, cross-sectional area of the cell, etc. The interaction of the cellular structure with the base is also explored, taking into account the above parameters. The results of laboratory studies on considering the interaction of the frame and backfill of the cell soil at different moisture content of the aggregate, taking into account the granulometric composition of the backfill soil surface tension of moisture contained in the soil, geometric parameters of the structure itself and a number of other factors.

Structural Mechanics of Engineering Constructions and Buildings. 2021;17(2):121-132
Structural analysis of high-rise building using ETABS and RSA software
Pechorskaya S.A., Galishnikova V.V., Gebreslassie S.B., Damir H.Y.
###### Abstract

There are numerous software applications available to analyze and design massive projects in short time. Most of the software have 2-dimensional and 3-dimen- sional tools, while various structural engineers employ the use of the 3D analysis and design tools in their day-to-day tasks because of its ease to operate and graphical user interface. These tools help in modeling, analyzing, and design of structures much more efficient. Despite the availability of numerous software products, there are confusions on the software to be used in the analysis and design of specific building structures. There is a need of studying the strength and weakness of some of these software tools to help structural engineers in the selection of the best application in their daily tasks. The aim of this study is to investigate the structural analysis of high-rise building with ETABS and RSA software and compare the influences of the structural analysis results from the two software in design. The comparison between the axial forces and moment from the results of ETABS and RSA software are presented. Case studies are considered to analyze the structure with the gravitational loads and lateral loads due to wind load by the two software applications. The case studies include a thirty-stories reinforced concrete building frame. The results of the analysis of the frame are compared and their difference is presented. From the analysis, the results show that, the moments and forces presented from RSA are bigger than that of ETABS.

Structural Mechanics of Engineering Constructions and Buildings. 2021;17(2):133-139
Optimization of channels and I-shaped bended closed profiles with tubular shelves from sheets of different thicknesses
Marutyan A.S.
###### Abstract

The continuation of optimization of channels and I-beams bent closed profiles (BCP) with tubular flanges made of rolled sheet of different thicknesses is presented. Such profiles are intended for light steel thin-walled structures (LSWS), which are distinguished by high technical and economic indicators and massive demand in industrial and civil construction, which confirms the relevance of their further development. The main results of the calculation of the optimal bending arrangement of composite sections of I-beams from sheet blanks of different thicknesses, including channel-type BCPs unified in terms of optimal parameters, are also presented. The aim of the study is to show that the characteristics of the LSWS can be further improved by shaping profiles, combining straight and round outlines of closed and open contours in a composite section. Methods. By means of experimental design studies, solution of optimization problems and variant design of I-profiles, their composite sections from sheet blanks of different thicknesses, including blanks of channel profiles, have been refined. The originality of channels and I-shaped BCP has been confirmed by patent examination. Results. The I-shaped BCP consists of two tubular shelves and one double thickness wall. Calculation of the optimal layout of an I-shaped BCP made of rolled sheet of different thicknesses for bending showed that the bearing capacity is limited by the ratio of the thickness of the flanges and the wall of its composite section. In particular, when the thickness of the flanges is 2 times the wall thickness, the strength is maximum at a ratio of width to height of 1/11, and when the thickness of the flanges is 0.6 times the wall thickness, the strength is maximum at a ratio of 1/3.3. With the ratios of the width and height of I-shaped BCP of 1/2.68...1/3 and channel-type BCPs of 1/5.36...1/6, their composite sections should be optimally assembled from standardized blanks.

Structural Mechanics of Engineering Constructions and Buildings. 2021;17(2):140-164
Theory of Thin Elastic Shells
The pendulum type surfaces with congruential cross sections
Krivoshapko S.N., Shambina S.L.
###### Abstract

The article discusses new kinematic surfaces that can be attributed to the class of surfaces of congruent cross sections. The surfaces of congruent cross sections were first identified in a separate class by Professor I.I. Kotov. Circular, elliptical and parabolic cylinders are taken as the guiding surfaces, and circles and parabolas are taken as generating plane curves, which can be located in the plane of the generating curve of the guiding cylinder or in a plane parallel to its longitudinal axis. The introduction of a new independent parameter helped to solve the set geometric problems. The analytical formulas are presented in generalized form, so the shape of the flat generatrix curve can be arbitrary. Two types of surfaces are considered: 1) when the local axes of the generating curves remain parallel during their movement; 2) when these axes rotate. The resulting surfaces can be of interest to architects, or can find application in machine-building thin-walled structures or in the study of the trajectories of bodies during their oscillatory-translational motion.

Structural Mechanics of Engineering Constructions and Buildings. 2021;17(2):165-174
Theory of elasticity
Areas of rational operation of steel rolling beams secured against curvatures
Golikov A.V., Veremeev D.V.
###### Abstract

Relevance. Beam cages are the most common type of floor covering for working areas of buildings and structures. Based on the results of a critical analysis of the existing methods for calculating and arranging the dimensions of beam cells, it was established that there are no clear recommendations on the rational range of selection of the sizes of beam cells depending on the surface load. The purpose of the study is to present the areas of rational operation of steel rolling beams, secured against buckling, based on the requirements of the calculation by the method of limit states. Methods. The tasks set in the work, aimed at achieving the research goal, are solved by analytical methods, relying on the basic laws of structural mechanics and existing knowledge about the actual operation of steel rolling beams under load. Methods of mathematical statistics were used to construct the main dependencies presented on the nomograms. Results. Areas of rational operation of steel rolling beams, secured against curvatures, are determined. The area of rational operation of beams is presented in the form of nomograms, which allow at the design stage to use a beam cell of maximum dimensions. As a criterion for rationalization, the criterion of the simultaneous satisfaction of the accepted section of the beam with the requirements of two groups of limiting states with minimum reserves was chosen. A refined algorithm for the layout of the beam cages and a refined method for calculating the cross-section of rolled beams are proposed, which make it possible to arrange the dimensions of the beam cage with a minimum steel consumption. The increase in the overall dimensions of the cells of the working platforms is substantiated.

Structural Mechanics of Engineering Constructions and Buildings. 2021;17(2):175-187
Seismic resistence
Seismic retrofitting of buildings using Building Information Modeling
Dereje L.S., Dabi G.M., Baza T.T., Rynkovskaya M.I.
###### Abstract

Building Information Modeling (BIM), in the last couple of decades, has emerged as a technology that can be used in combination with different methodologies in the fields of architecture, engineering, and construction industry as a digital model to facilitate the planning and design process, construction and maintenance. Using the tools of BIM, the stakeholders generate the digital models that can help them to identify the problems. A total of 24 conference papers, referenced journal articles, and other academic sources were analyzed based on their relevance and research focus areas. This article provides a review on the integration of building information modeling with different methodologies for seismic retrofitting of both structural and non-structural components of buildings. Pre-seismic and post-seismic applications of Building Information Modeling with the integration of different methodologies have been reviewed overbuilding life cycles with a view of addressing the challenges and recommending the future research perspectives. In the end, by stating the possibilities of integration of BIM tools with different methodologies mainly using Performance-Based Earthquake Engineering as a paradigm which is fully probabilistic, this paper concludes that the implication of the Building Information Modeling with the integration of different methodologies isn’t merely the inclusion of the certain conditions, but also of the numerical integration of all the possible uncertainties.

Structural Mechanics of Engineering Constructions and Buildings. 2021;17(2):188-198
Experimental researches
The probability of the existence of defects that lead to the destruction of the pressure vessel without leak
Kuzmin D.A., Vertashenok M.V.
###### Abstract

Relevance. To ensure the safety of a nuclear power plant on the basis of the requirements of norms and rules in the field of the use of atomic energy for pipelines of the primary circuit of a nuclear reactor, the design should apply the leak before break concept. The main idea of the concept is to prevent a sudden rupture of the pipelines of the reactor coolant loop, and consists in substantiating the fact that the rupture is preceded by the formation of a stable through crack, which is detected by the provided leak control means. When substantiating the concept, it is assumed that “break without leak” is an impossible event. This article provides a method for determining the probability of a failure event without a leak. Purpose - estimate the probability of the existence of a defect that can lead to the destruction of the vessel or pressure pipeline without leakage, as well as the probability of failure without leakage for a known number of loading cycles. Methods. To systematize the data obtained by different methods of non-destructive testing, conservative assumptions were used to determine the area of detected defects. On the basis of the obtained defect sizes, the defect size regions were determined, which can determine the scenarios of crack growth. Using the methods of mathematical statistics, the probability of the existence of a defect, which can lead to failure without leakage, was determined. Based on the methods of the theory of reliability, a comparison of the obtained probability of destruction with the admissible value is carried out. Results. A method for processing non-destructive testing data based on an assessment of the area of detected defects has been developed to systematize the data obtained by different non-destructive testing methods. The criterion for the development of cracks according to the scheme “leak before destruction” is determined. A method has been developed for determining the probability of a defect that can lead to failure without leakage. An example of calculation based on feed water pipelines is considered.

Structural Mechanics of Engineering Constructions and Buildings. 2021;17(2):199-213