# Vol 14, No 6 (2018)

**Year:**2018**Articles:**10**URL:**https://journals.rudn.ru/structural-mechanics/issue/view/1155**DOI:**https://doi.org/10.22363/1815-5235-2018-14-6

## Full Issue

## Numerical methods of structures’ analysis

### Effect of stress concentration in a beam of rectangular cross section in the region of attachment of the longitudinal efforts

#### Abstract

Relevance. To ensure the safe operation of buildings and structures, it is necessary to more accurately determine the stress-strain state (SSS) of structural elements, to identify areas of stress concentration. The distribution of stresses in the region of the fastening bars in three-dimensional formulation is relatively little studied. In these areas, there may be significant stress concentrations that contribute to the occurrence and development of cracks and splits, which are a harbinger of destruction. The development of modern methods of calculation, software systems and the growth of computing capabilities allow refining the design scheme: to move from one-dimensional to two-dimensional calculation scheme, from two-dimensional to three-dimensional calculation scheme. All this makes it possible to more accurately assess the SSS of structural elements and structures, to identify areas of stress concentration, as well as to investigate the effect of the Poisson's ratio on the stress concentration. Methods of research. It is noted that cracks and breaks in the edges under the influence of longitudinal loads occur in the rods (racks) of square cross-section. Three-dimensional elements based on the spline version of the finite element method and the LIRA computational complex are used to estimate the stress-strain state. The spline finite element method, thanks to the synthesis of the idea of parametrization and the finite element method (FEM) with cubic approximation of all three required variables within each element, allows obtaining consistent three-dimensional finite elements. On the basis of the mentioned methods and complexes, numerical studies of the stress concentration in the bars of square and rectangular cross-sections fixed at one end and perceiving the tensile forces at the other end are performed. Conclusions. It is found that in the angular points of the cross section in the area of fastening of straight bars, perceiving axial tensile forces, there are stress concentrations. Away from the mounting area of the bar, the voltages are aligned. By increasing the Poisson's ratio, the stress concentration increases faster than at low values. The transition from a onedimensional design model to a two-dimensional one, and even more so to a three-dimensional model allows to determine the stress concentration, both in plan and in thickness. Information about the concentration of stresses in elements of structures will allow designers to more accurately design structures and facilities, and the operators to promptly identify the defective region.

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(6):451-458

### Comparative analysis of efficiency of use of finite elements of different dimensionality in the analysis of the stress-strain state of thin shells

#### Abstract

Relevance. To determine the stress-strain state (SSS) of thin-walled shells due to the complexity of obtaining numerical results, the theory of thin shells was developed with the introduction of the direct normal hypothesis to reduce the three-dimensional SSS to the two-dimensional one. With the modern development of digital technology and numerical methods of calculation, in particular the finite element method (FEM), it became possible to obtain numerical results without the use of the direct normal hypothesis, namely on the basis of the theory of elasticity in three-dimensional formulation even for thin shells. Aims. The aim of this work is to compare the efficiency of algorithms for the use of finite element stiffness matrices obtained on the basis of the theory of thin shells with the hypothesis of a straight normal and on the basis of the relations of the three-dimensional theory of elasticity. Methods. The results of comparative analysis of finite element calculations of thin shells using a two-dimensional sampling element in the form of a quadrangular fragment of the middle surface and a three-dimensional element in the form of an eight-node six-face are presented. The components of the displacement vector and their first derivatives were chosen as the nodal variable parameters. The functions of the form for both types of discretization elements were represented by products of Hermite polynomials of the third degree. Results. On the example of calculation of the cylindrical shell clamped at the ends it is shown that the two-dimensional statement in calculations of thin shells is adequate and allows to receive acceptable results at optimum costs of machine time.

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(6):459-466

## Analysis and design of building structures

### Numerical simulation of the front of an air shock wave in a ground and air explosion in the software package LS-DYNA

#### Abstract

Introduction and objectives. When calculating buildings and structures for special combinations of loads caused by the action of air shock waves, it is necessary to determine the main parameters of the actual load. The regulatory approach implemented in modern regulatory documents proposes the use of simplified calculation methods based on the use of equivalent static loads. The aim of the study is to obtain the basic parameters of air shock waves, as well as to consider the nature of the propagation of the shock wave front during an explosion on the ground and in the air, using numerical simulation. Materials and methods. To obtain the basic parameters of air shock waves, high-precision numerical methods implemented in the modern LS-DYNA software package are considered. To describe the explosion process, the LagrangianEulerian approach is used. Results. Isopoles and graphs of excess overpressure Δ Р ф over atmospheric pressure in an air shock wave were obtained when the epicenter of the explosion was located at ground level and in the air, as well as at a distance from the designed structure. Conclusions. The considered method of numerical simulation allows to obtain the main parameters of air shock waves, which can be used for further calculation of building structures.

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(6):467-474

### Application of plate mechanics to evaluate the effectiveness of reinforcing shot blasting

#### Abstract

Introduction. The paper considers the current state in the field of surface plastic deformation, namely the hardening of machine-building parts by shot blasting. Since modern engineering uses improved technological methods and methods for transforming material parts into a state that meets the standards for the operation of products, in the domestic and foreign literature there are many ways to assess the impact of operating conditions on the part life. However, the fundamental underlying theory of this field has not yet been created. The article describes the essence of the process of surface plastic deformation. The types and advantages of shot blasting are also considered. Many readers may wonder: is it possible, after removing the corrosion layer, to strengthen the surface layer of the workpiece? The method of shot blasting copes well with these diverse tasks, allowing to handle parts of complex geometry, as well as parts with hard-to-reach places. The quality of processing allows to apply any coating to the surface of a part without additional preparation and degreasing. Aims. One of the problems is the difficulty of determining the level of residual stresses generated in the process of shot blasting. The significance of the problem lies in the fact that at present there is no exact method for determining residual stresses after shot peening. The purpose of this study is to evaluate the effectiveness of shot peening, i.e. determination of the level of residual stresses generated in the process of shot blasting. The task is to determine the residual stresses during shot blasting by measuring the deformation of the control plate (witness sample) obtained by one-sided bead over a certain period of time. Methods. After processing, the deflection of the control plate is determined. According to the deflection arrow, the residual stresses in the plate are determined. To do this, the N.N. Davidenkov’s method is used, according to which a strip is cut out from the control plate and the layers are removed by etching. When removing the layers, the strip changes the geometry due to a change in the stress state, which makes it possible to determine the distribution of the residual stresses of the plate using the appropriate ratios. The objective of the proposed technique is to simplify the method, reducing the complexity of determining the distribution of residual stresses across the thickness of the control plate, improving the accuracy of determining the residual stresses during shot peening. Conclusions. Thus, based on the positions of the mechanics of plates, the deformed state of the control plate during shot blasting was considered. Finally, an analytical dependence was obtained, allowing estimating the residual stresses in the control plate after shot blasting.

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(6):475-480

### Behavior of the frames of large-span metal domes in the process of their installation

#### Abstract

Goal. The goal of this paper is to characterize the process of forming the frames of large-span metal domes during assembly process. The load-bearing structural schemes during the assembly of frames differ from those, adopted for their analysis and design. Due to this fact, initial internal forces appear in the structural elements of frameworks that are called assembly forces. Geometric schemes of dome frameworks and the principles of their formation are described for ribbed domes, ribbed domes with annular rings and lattice domes. It is shown how lattice dome frameworks are formed and why they are considered as spatial bar systems. Specific features of the structural solutions for single-layer and double-layer frameworks are described. It is noted that the technological scheme for the assembly of structures of large-span metal domes depends on the structural systems of frameworks and on the methods of their erection. A brief description is given of differrent methods for erecting frameworks of large-span metal domes and of the number of temporary supports and mechanisms used in this process. Review. Different methods of erection are illustrated with the examples of several well-known dome structures built in the world. The evaluation of the influence of each process on the behavior of structures during the installation is given. The nature of the work of individual structures and a frame is described for the process of erecting large-span metal domes. The emphasis was made on the significant differences in the nature of work of structural systems of dome frame-works with different ways of their installation. Research. Computer models of the lattice metal domes are made of steel I-bars with rigid connections at the joints. Additional models were created for incomplete frameworks to study alternative ways of erection. For each assembly model of the dome framework, computer analysis was performed for the action of its self-weight. Stresses in the structural members, obtained as a result of the analysis, were compared with the stresses in the corresponding elements of the design model of the framework under the self-weight. Conclusions. The conclusion is made that the stresses in the elements of frameworks of the large-span metal domes are unavoidable when they are erected. The necessity of compulsory analysis of frameworks for erection conditions in the design of large-span metal domes was noted.

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(6):481-494

### The development of chart based method for steel beam designs using the Russian sections

#### Abstract

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(6):495-501

## Theory of Thin Elastic Shells

### Geometric modeling and linear static analysis of thin shells in the form of cylindroids

#### Abstract

Aims. Thin shells in the form of cylindroids are fourth-degree ruled shells for which few works are devoted. In this paper, their geometric modeling is worked out and their middle surface are plotted, using the software MathCAD. Their stress-strain state are instigated with two building material: reinforcement concert and qualitative steel. Methods. This linear investigation is done for fixed and hinged supports and for various thicknesses in the software SCAD. The numerical values of their maximum and minimum displacements of their middle surfaces are given. Based on these displacements, conclusions are made for the whole paper. Results. The linear analysis for reinforced concrete and metallic shells, computed using the software SCAD gives the numerical and graphical results that are presented. Conclusions. The investigations of the stress-strain state are done for shells with the shape of cylindroid with two directrices ellipses and cylindroid Frazer. For the same thickness, loading and span, the reinforced concrete shells has minimum displacements. For thickness, 20 cm the steel shells have the same maximum displacements. For the thickness 30 cm the maximum displacement is more in steel shells. It is more optimal to use reinforced concrete shells than the one in steel. A large span (till 30 m) shells can be designed with reinforced concrete.

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(6):502-508

### Complicated features and their solution in analysis of thin shell and plate structures

#### Abstract

Introduction. It is instructive to assemble a list of applications from a historical point of view, and to take as a connecting theme the way in which the introduction of the thin shell as a structural form made an important contribution to the development of several branches of engineering. The following is a brief list, which is by no means complete and complicated features and their solutions for analysis of such structures. Solution technique, methods. The linear theory of thin elastic shells with arbitrary shape of the middle surface is derived on the basis of Kirchhoff’s assumptions that were used in the development of the plate bending theory introduced in Part I. These assumptions are formulated for the linear theory of thin shells of an arbitrary shape. The problem of the study of this article is to identify simple way of solution to analyze complicated features of thin shell structure by introducing modern and new programmable theories and aspects. Especially the intersecting line of connecting thin shell structures. Results. It is possible to successfully model explicitly a panel profile that can be used for optimization studies for use as possible future test studies. It has also been shown, that if test data exists, a numerical solution can be very accurately modeled to match the test data by modifying the material properties of the model. Discussion. The article should encourage structural engineers to solve complicated features in thin shell structures and design for construction of such structure which are rarely constructing in country like Nepal due to lack of skilled manpower.

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(6):509-515

## Problems of theory of elasticity

### Flat geometric-nonlinear shear strains

#### Abstract

Aims. The problem of differential equation construction characteristics and balances is being analyzed; and also the definitions of the planar wave rotational deformation travel time in the continuum, the mechanical character of which is described by the mathematical models geometrically nonlinear analogues in continuous body, the stress-strain stain of which is described by the undefined, basically, by the cross-connections between the first tensor invariant and the second invariant deviator of the stresses and nonlinear deformations. Methods. As an example let’s plot the specific speed of the transverse waves depending on the intensive rotational transverse deformation and the meanings of the material mechanical constants for the three mathematical models of the continuum: model 1 corresponds to the geometrically nonlinear analogue of the elasticity linear theory; model 2 corresponds to the geometrically nonlinear analogue of the small quantity elastoplastic strain theory; model 3 corresponds to geometrically nonlinear analogue of deformation theory of the loose medium plasticity. Conclusions. It is stated that in half-subspace the mechanical behavior of which is described by the deformation theory equations of the loose medium plasticity, the shock waves can appear in continuous boundary conditions.

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(6):516-522

## Experimental researches

### Mathematical models of multi-barreled construction artillery systems

#### Abstract

The article presents the schematic diagrams and mathematical models of multi-barrel artillery systems designed for shooting and extraction of building elements from the ground, describes the results of numerical experiments carried out on the basis of the proposed mathematical models and allow to study the dynamics of multi-barrel building artillery systems during the shot. Mathematical forecasts on the depth of piles in the soil, the maximum pressure in the channels of the stems, the magnitude and speed of the guns rollback for different conditions of loading the stems and their technical characteristics are described. As a verification of the proposed mathematical models, the results of experiments for singlebarrel artillery guns, which are a special case of multi-barrel guns, are described.

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(6):523-532