# Vol 16, No 4 (2020)

**Year:**2020**Articles:**8**URL:**https://journals.rudn.ru/structural-mechanics/issue/view/1357**DOI:**https://doi.org/10.22363/1815-5235-2020-16-4

## Full Issue

## Analysis and design of building structures

### Modeling of random static loads on a structural cover with limited statistical data

#### Abstract

**Structural Mechanics of Engineering Constructions and Buildings**. 2020;16(4):243-249

### Modeling of a piled foundation in a Femap with NX Nastran

#### Abstract

Relevance. The underground part of the building (foundation and soil) has a significant impact on its stress-strain state and behavior under the influence of operational loads. Therefore, the existing regulatory and technical documentation regulates the design of buildings (structures), taking into account the joint work of their aboveground and underground parts. In practice, such accounting becomes possible on the basis of a comprehensive engineering analysis of the building as a large mechanical system “building - foundation - soil”, which today can be carried out using the finite element method. In the case of pile foundations, the correctness of the result depends largely on the reasonable choice of the design model of the pile-soil subsystem. The article analyzes three design models of piles operating in an array of soil foundation. The first model is discrete. In it, the pile is modeled by bars and is based on elastic supports (Spring) with generalized stiffnesses. Second model - spatial, in which the pile and soil are typed in by volumetric elements (Solid). Third model - spatial-bar or combined, in which the bar pile is embedded in the mesh of the soil mass using a rigid substructure formed by bars of high rigidity. The aim of the work - to determine a rational calculation model of the “pile - soil” subsystem, which allows, on the one hand, to reduce the general order of the system of resolving equations, and, on the other hand, to maintain the accuracy of the assessment of the stress-strain state of the calculation model of “pile - soil” and the building as a whole. Materials and methods. The numerical results of the analysis of the pile foundation statics using the three “pile - soil” calculation models were performed in the CAE software package - the Femap with NX Nastran class, which implements the finite element method. Results. Comparative-numerical analysis of the stress-strain state of the “pile foundation - soil” subsystem made it possible to determine the advantages, disadvantages, and also the areas of rational use of bar, spatial combined calculation models. In the next articles, it is planned to consider the calculation of piles for vertical loads, as well as a comparative analysis of numerical results with experimental data (in the labo-ratory or in field conditions) for horizontal and vertical effects.

**Structural Mechanics of Engineering Constructions and Buildings**. 2020;16(4):250-260

## Numerical methods of structures’ analysis

### Choice of mathematic models of soils in static and seismic analyses of embankment dams

#### Abstract

Relevance. Numerical analyses of behavior or stress-strain state (SSS) of embankment dams are usually performed using various computational programs, which use different, often complex mathematical models of soils. However, the right choice of these models is left to the program user, who usually has not enough experience in this field of knowledge, and therefore the results of these analyses are often obscure and erroneous. The aims of the work - development of recommendations for selecting the most reliable mathematical models of soils in numerical analyses of embankment dams and comparing these models with the most common models in modern world practice of their application. Methods. Deep comparative analysis of many soil models was conducted on the use of the soil models in numerical analyses of embankment dams during author’s work in ICOLD Committee on Analysis and Dam Design. Results. On the basis of the evaluation of the reliability of soil models, recommendations were obtained on the choice and application of these models in the numerical analyses of SSS of embankment dams under action of static and seismic impacts; interactions between the results of these analyses and dam monitoring data were identified.

**Structural Mechanics of Engineering Constructions and Buildings**. 2020;16(4):261-270

## Geometrical investigations of middle surfaces of shells

### The opportunities of umbrella-type shells

#### Abstract

Relevance. The necessity of division of umbrella surfaces and surfaces of umbrella type into two separated classes is explained in introduction. Earlier, umbrella surfaces and surfaces of umbrella type were in the same class of surfaces because they consist of the identical fragments lying on the surfaces of revolution. Umbrella surfaces are compound surfaces on the base surface of revolution but umbrella-type surfaces are kinematic surfaces formed by continuous movement of a changing curve and that is why taking into account the methods of construction of these surfaces they were divided in two separate classes. The aim of the work is a collection of main publications on all areas of the investigation of umbrella-type shells. Methods. For the determination of principal results of investigation of umbrella-type shells, it is necessary to know differential geometry of surfaces, structural mechanics of thin shells, and approaches used in architecture of spatial structures. Results. In this article, the principal scientific papers on geometry, strength analysis, and offers of applications of thin-walled shells of umbrella type in building and of reflectors of umbrella type for space apparatuses. The accurate parametric equations of some determined surfaces are presented. The approximated computer models of middle surfaces of the real umbrella shells but in the form of umbrella-type surfaces are given. The examples of determination of stress-strain state of thin-walled shells of umbrella type without dividing of the whole shell in identical fragments are shown. New information and materials already known about shells of umbrella type give reasons to suppose that the shells of this type will be claimed by engineers and architects.

**Structural Mechanics of Engineering Constructions and Buildings**. 2020;16(4):271-278

### Visualizing surface formation of semi-regular polyhedra of Archimedes

#### Abstract

The most common method of forming semi-control polyhedra consists in cutting off angles and ribs of regular polyhedra by planes. The aim of the work - to consider the automated formation of a number of surfaces of semi-regular Archimedean polyhedra based on the dodecahedron. These include the truncated dodecahedron, the icosododecahedron, the romboicosododecahedron and the truncated icosododecahedron. The formation of surfaces is carried out by the kinematic method in AutoCAD using programs compiled in the AutoLISP language. Methods. The methodology for the formation of these polyhedra provides for truncation of the angles and edges of the dodecahedron. This requires the calculation of a number of geometric parameters of these polyhedra and dodecahedron, such as the value of the truncation of the dodecahedron edges, the size of the edges of truncated polyhedra, the centers of faces, dihedral angles, etc. In order to generate these surfaces, a frame is constructed because the frame lines are used as guides to form surfaces in a kinematic way. The electronic model of each polyhedron is constructed as a set of compartments of surfaces of all its faces, and each compartment is assigned to a certain layer of the drawing. The frame and electronic model of the polyhedra under study are formed by means of user programs composed in the functional language AutoLISP. The process of forming surfaces of selected polyhedra in the AutoCAD environment is provided by special programs that are also compiled in the AutoLISP language. Results. Software was created to demonstrate the process of formation of a number of Archimedes polyhedra on the monitor screen.

**Structural Mechanics of Engineering Constructions and Buildings**. 2020;16(4):279-289

## Experimental researches

### Results of experimental studies of high-strength fiber reinforced concrete beams with round cross-sections under combined bending and torsion

#### Abstract

The aim of the work - experimental investigation on crack propagation and deformation in high-strength fiber reinforced concrete beams with round cross-sections under combined bending and torsion for the development of practical methods of crack resistance, deformation and strength analysis of such structures, and also for the accumulation of new experimental data on resistance under combined loading. Method is experimental-theoretical. Results. Deflection plots and force-deformation relationships for high-strength fiber reinforced concrete beams with round cross-sections under combined bending and torsion are determined experimentally. Principal deformations in terms of elongation and compression of concrete for the experimental beam structures with high torsion to bending moment ratio are determined. It is established that for high-strength fiber reinforced concrete structures of circular cross-section, generally, development of one-two discrete cracks is observed, therefore the circular shape of the cross-section slightly reduces the concentration defined by the material structure of high-strength concrete. On the basis of the conducted investigation on high-strength fiber reinforced concrete structures with circular sections, new experimental data on the combined stress-strain state in the studied areas of resistance is obtained, such as: values of generalized cracking, and failure, load, its level relative to the ultimate load; distance between the cracks at different stages of crack propagation; crack widths at principal reinforcement axis level, at a double diameter distance from the principal rebar axes and also along the entire crack profile at various stages of loading; coordinates of nonplanar crack formations; patterns of crack formation, development and opening in reinforced concrete structures under combined bending and torsion.

**Structural Mechanics of Engineering Constructions and Buildings**. 2020;16(4):290-297

## Dynamics of structures and buildings

### Influence of the foundation bed stiffness on the dynamic properties of the building as of a multi-mass cantilever bar

#### Abstract

Relevance. The study of the interaction of buildings and structures with the base during an earthquake is one of the most important tasks of the theory of earthquake resistance. The response of the structure to seismic impact depends to a large extent on the ratio of the stiffness characteristics of the soil, foundation, and foundation structure. Moreover, taking into account a rather high degree of statistical variability of the characteristics of the soil foundation, it is possible to ensure the required level of safety of a structure only through the use of probabilistic models and a quantitative assessment of the reliability of the construction-base system as a whole. At present, for the calculation of the “construction - base” system for seismic loads, deterministic discrete models of the finite element method are mainly used. But these models are poorly adapted for probabilistic calculations and require extensive statistical data, which are currently insufficient. Therefore, in problems of reliability assessment, it is advisable to use simplified analytical models, which make it possible to derive the value of the statistical variability of its reaction with relatively small initial information about the system. The aim of the work - based on the well-known solution for the single-mass model to present an analytical solution in the matrix form of the problem of free horizontal vibrations of a multi-mass cantilever rod on the foundation specified by the elastic half-space model. Methods. A study was made of the effect of the compliance of the soil foundation on the frequencies and forms of horizontal vibrations of the structure. A comparison of the results with the calculation performed by the finite element method is given. Results. The obtained solution is intended to conduct a probabilistic calculation of the construction-base system under seismic loads and evaluate its reliability.

**Structural Mechanics of Engineering Constructions and Buildings**. 2020;16(4):298-310

## Theory of elasticity

### Stressed state of two-layer strip when interacting with rigid base

#### Abstract

Relevance. In the calculation of multilayer bases, when the material of one or several layers has a pronounced anisotropy, the nature of the distribution of displacements and stresses depends on the direction of the anisotropy axes in each layer. Therefore, it is necessary to have an evaluation of the influence of this factor in the design and analysis of the operation of multilayer media. The aim of the work - to research the stress state in a strip composed of two anisotropic plane-parallel layers with different physical characteristics, lying without friction on a rigid base. Methods. The integration of the equations of the plane problem of the theory of elasticity of an anisotropic body is carried out by the symbolic method in combination with the method of initial functions. The initial functions on the contact line of the strip and the base are determined from the conditions of tight adhesion between the layers, the conditions of tight contact and the absence of friction between the strip and the base, the nature of the load applied to the upper plane of the strip. After transformations, the functions of displacements and stresses in each layer are written through the normal surface load in the form of improper integrals. Results. Plots of changes in stresses in the strip from the values of the characteristics of anisotropic materials, layer thicknesses are given. The maximum stresses on the interface line of the layers and on the line of contact with the base, depending on the direction of the anisotropy axes in each layer, are presented in the tables and shown in graphs. The effect of the elastic modules of materials on the nature of the stress distribution in a strip composed of two isotropic materials is estimated.

**Structural Mechanics of Engineering Constructions and Buildings**. 2020;16(4):311-319