# Vol 16, No 1 (2020)

**Year:**2020**Articles:**10**URL:**https://journals.rudn.ru/structural-mechanics/issue/view/1289**DOI:**https://doi.org/10.22363/1815-5235-2020-16-1

## Full Issue

## Articles

### ANNIVERSARY OF PAVEL M. SALAMAKHIN

**Structural Mechanics of Engineering Constructions and Buildings**. 2020;16(1):3-4

## Analysis and design of building structures

### Substantiation of the necessity and method of upgrading the software of the measuring complex for assessing the load capacity of girder spans of road bridges

#### Abstract

The article notes that the software of the complex used in the Russian troops to solve in a short time the actual problem of determining the possibility of safe passage of super heavy loads on girder road bridges has the following disadvantages: 1) it can only be used for split concrete bridges; 2) the decision to pass a large load through the bridge is made only by the value of the deflection in the center of the span, without taking into account the resulting stresses in the bridge span structure structures, and without taking into account the bearing capacity of the supports. In the article, in order to eliminate these shortcomings: 1) a strict formula is obtained for calculating the deflection in the middle of beam spans made of any structural materials from the angle of rotation of their support sections; 2) based on the use of the fundamental relationship between the relative heights of girder spans, the relative deformations of the edges of their cross sections and their relative deflections, it is proved that the maximum stresses in the edges of the cross sections of girder spans from any structural materials can be calculated by the maximum deflection value in the middle of their spans; 3) a method is established for determining the ability of beam bridge supports to ensure safe passage of a heavy vehicle by the nature of changing the rotation angles of the supporting cross sections of the span structures under the influence of the movement of the heavy vehicle layout. Taking these three results into account, when upgrading the software of the measurement system, ensures that the goal of the work is achieved.

**Structural Mechanics of Engineering Constructions and Buildings**. 2020;16(1):5-13

### The effectiveness of the implementation of pile foundations on the example of the reactor building of a nuclear power plant with VVER-1000

#### Abstract

Aims. The purpose of this work is to justify the reliability of the developed models of pile foundations on the data of field observers and to demonstrate the feasibility of using pile foundations to increase the stability and bearing capacity of the NPP structures foundation using the example of reactor building (RB). Methods. The data of field observers for the settlement of the RB are presented. The expressions for calculation of the static stiffness of the contact surface of the slab bottom and soil medium, as well as for pile foundations taking into account the effects of interaction of grillage and pile field with the soil media with a general character of displacement of a circular cross section pile are submitted. A spatial three-dimensional finite element static model of RB was developed together with the soil base. Isolines of vertical movements of RB fundamental slabs for natural foundations, as well as for pile foundations for normal operation are shown. A comparative analysis of the data of field observers with the calculation results allows us to justify the reliability of the developed model of the pile foundation. Results. The calculations of the foundation yield correspond to all the period of operation including construction, and the results of observations relate only to the period of operation that explain the difference. A comparative analysis of the data of field observers with the calculation results allows us to justify of the strong effectiveness of realization of pile foundation for the massive structures on soft soil bases.

**Structural Mechanics of Engineering Constructions and Buildings**. 2020;16(1):14-21

### Effect of joint stiffness and flexibility on the design of reinforced cement concrete structure

#### Abstract

Relevance. A beam-column joint is a crucial zone in any frame structure that transmits the forces at the end of the members in the panel zone. The connection between the joints may be assumed as rigid or flexible one and it is not an ideal one to predict the actual behavior of the joint section. Methods. The displacement along the joint section is the most critical one that has to be taken care while designing the structure. In this paper, the flexibility of the reinforced concrete joints was studied under two different cases: in first phase, building having 3 storey including ground floor was taken and is analysed using SAP 2000 and secondly third floor shear wall with l hollow concrete mesh of column section was analyzed in same software and the flexibility of the joints was tested in terms of its stress and displacement parameters using different approaches such as link mass property, end length offset zone, panel zone rotational spring stiffness property. The results obtained from the two cases were analyzed with consideration of parametric study and variation of the stresses with displacement and are shown with comparative graphic.

**Structural Mechanics of Engineering Constructions and Buildings**. 2020;16(1):22-30

## Theory of thin elastic shells

### Accounting for geometric nonlinearity in finite element strength calculations of thin-walled shell-type structures

#### Abstract

Relevance. Currently, in connection with the wider spread of large-span thinwalled structures such as shells, an urgent issue is the development of computational algorithms for the strength calculation of such objects in a geometrically nonlinear formulation. Despite a significant number of publications on this issue, a rather important aspect remains the need to improve finite element models of such shells that would combine the relative simplicity of the resolving equations, allowance for shear deformations, compactness of the stiffness matrix being formed, the facilitated possibility of modeling and changing boundary conditions and etc. The aim of the work is to develop a finite element algorithm for calculating a thin shell with allowance for shear deformations in a geometrically nonlinear formulation using a finite element with a limited number of variable nodal parameters. Methods. As research tools, the numerical finite element method was chosen. The basic geometric relations between the increment of deformations and the increment of the components of the displacement vector and the increment of the components of the normal vector angle are obtained in two versions of the normal angle of the reference. The stiffness matrix and the column of nodal forces of the quadrangular finite element at the loading step were obtained by minimizing the Lagrange functional. Results. On the example of calculating a cylindrical panel rigidly clamped at the edges under the action of a concentrated force, the efficiency of the developed algorithm was shown in a geometrically nonlinear setting, taking into account the transverse shear strain.

**Structural Mechanics of Engineering Constructions and Buildings**. 2020;16(1):31-37

### Geometric characteristics of the deformation state of the shells with orthogonal coordinate system of the middle surfaces

#### Abstract

The aim of this work is to receive the geometrical equations of strains of shells at the common orthogonal not conjugated coordinate system. At the most articles, textbooks and monographs on the theory and analysis of the thin shell there are considered the shells the coordinate system of which is given at the lines of main curvatures. Derivation of the geometric equations of the deformed state of the thin shells in the lines of main curvatures is given, specifically, at monographs of the theory of the thin shells of V.V. Novozhilov, K.F. Chernih, A.P. Filin and other Russian and foreign scientists. The standard methods of mathematic analyses, vector analysis and differential geometry are used to receive them. The method of tensor analysis is used for receiving the common equations of deformation of non orthogonal coordinate system of the middle shell surface of thin shell. The equations of deformation of the shells in common orthogonal coordinate system (not in the lines of main curvatures) are received on the base of this equation. Derivation of the geometric equations of deformations of thin shells in orthogonal not conjugated coordinate system on the base of differential geometry and vector analysis (without using of tensor analysis) is given at the article. This access may be used at textbooks as far as at most technical institutes the base of tensor analysis is not given.

**Structural Mechanics of Engineering Constructions and Buildings**. 2020;16(1):38-44

## Numerical methods of structures’ analysis

### Study of modern software capabilities for complex shell analysis

#### Abstract

Relevance. In design and calculation of civil engineering structures, several standard commercial software packages, which are successfully applied to solve everyday engineering problems, are traditionally used. However, when it is necessary to design the models of complex shape shell structures with defining surfaces based on parametric equations, such programs often have certain drawbacks. The aim of the work - analysis of existing types of commercial computational software packages in order to check which allow to design finite element models for shell structures with median surfaces of complex geometry given by parametric equations. Methods. The analysis of commercial computational software packages is carried out by studying the software manuals, and by building and calculating a model in the shape of a right helicoid as a test example. To evaluate the results of the stress-strain state of a shell with a middle surface in the form of a right helicoid, an analytical calculation method based on the Reissner’s equations and Fourier series expansion is used. Results. A review of modern commercial computational software packages as applied to models defined by parametric equations is carried out. A model for a shell structure with a median surface in the form of right helicoid is built. The numerical results of stress-strain behavior of the right helicoid are obtained and analyzed in comparison with the analytical solutions obtained using the Reissner’s equations with Fourier series expansion. The pros and cons of several popular means of software are presented.

**Structural Mechanics of Engineering Constructions and Buildings**. 2020;16(1):45-53

### Numerical analysis of stability of the stiffened plates subjected aliquant critical loads

#### Abstract

The aim of the work is to research the precritical and postcritical equilibrium of the stiffened plates subjected aliquant critical loads. Methods. The finiteelement complex MSC PATRAN - NASTRAN was used in the paper. To simulate the plates, flat four-node elements were used. Calculations taking into account geometric nonlinearity were carried out. The material of the shells was considered absolutely elastic. Results. A technique has been developed to study the stability of reinforced longitudinally compressed plates; the critical forces of the stiffened plates of various thicknesses had been calculated. Graphs of deflections dependences on the value of the compressive load had been constructed. The influence of initial geometric imperfections on the value of the critical loads for stiffened plates has been investigated.

**Structural Mechanics of Engineering Constructions and Buildings**. 2020;16(1):54-61

## Dynamics of structures and buildings

### New operational ratios and their application to non-stationary tasks for rods based on S.P. Timoshenko theory

#### Abstract

Relevance. In order to study transient wave processes of deformation in rods on the basis of S.P. Timoshenko theory, it is necessary to have accurate analytical solutions to non-stationary problems in general form. Each accurate solution within this analytical model is an accurate description of the real process, serves as a criterion in assessing the accuracy of approximate solutions. When using operational calculus to analyze traveling waves, it is the inverse Laplace - Carson transformation that poses the greatest difficulty. It follows from the published works that the available solutions to some private problems either have a structure that does not allow to judge the main features of the investigated process, or their efficiency in calculations is achieved only in some rather limited areas of coordinate and time. This problem, which requires resolution, determined the purpose of this article. The aim of the work. The article is devoted to the development of new operational ratios and their application to the construction of accurate analytical solutions to the non-stationary problems of S.P. Timoshenko's theory for rods in a general form, in a physically visible and convenient form for practical calculations. Methods. The work uses methods of function theory of complex variable, operational calculus based on the integral Laplace - Carson transformation, methods of structure dynamics. Results. In general form three types of non-stationary tasks for semi-infinite rod based on Timoshenko theory are formulated. New operational ratios have been obtained. Based on these ratios, a method of inverse transformation without using a general conversion formula has been developed. Solutions of problems are recorded in the form of integrals from Bessel functions and, unlike solutions available in the literature, clearly show the wave nature of the studied processes, have a visual and compact appearance. An example of calculation is reviewed.

**Structural Mechanics of Engineering Constructions and Buildings**. 2020;16(1):62-75

## Seismic resistence

### Earthquake resistance analysis of structural systems of multi-storey civil buildings

#### Abstract

Relevance. Increasing the density of urban population requires the use of optimal structural systems of multi-storey civil buildings, however, despite a large number of studies on the rationality of their application, the question of choosing an assessment of seismic resistance of structural systems of multi-storey civil buildings is still open. The aim of the study. This study aims to determine advantages and disadvantages of structural systems of multi-storey buildings in seismic areas. Methods. The results of comparison analysis of five structural systems (columns grid - 6×6 m, storey height - 3 m, number of storeys - 20) are presented in this article. The structural systems are: frame & tube, frame & core, core & walls, framed core & walls, framed core & tube. The calculation were done according to Building Code 14.13330.2018 for an earthquake of 8 points intensity of MSK-64 intensity scale. The SCAD Office software package was used for modeling and analyzing. The sum of the effective modal masses taken in the calculation was at least 90% of the total mass of the system excited in the direction of the seismic action for horizontal impacts and at least 75% - for vertical impacts. Results. The comparison was carried out according to the following criteria: maximum displacements, maximum compressive and tensile stresses, maximum periods of natural oscillations, maximum accelerations.

**Structural Mechanics of Engineering Constructions and Buildings**. 2020;16(1):76-82