# Vol 14, No 1 (2018)

**Year:**2018**Articles:**10**URL:**https://journals.rudn.ru/structural-mechanics/issue/view/1041

## Full Issue

## Analytical reviews

### LARGE-SPAN METAL DOME ROOFS AND THEIR CONSTRUCTION

#### Abstract

The article presents the main types of geometrical and structural systems of steel frameworks of metal dome roofs. Based on the geometrical system, three main types of metal domes can be specified: ribbed domes, ribbed domes with rings, and lattice domes. Lattice domes can be cyclically symmetrical with repeating sectorial patterns, or geodesic, that are based on geodesic polyhedrons, inscribed in a sphere. Based on the structural system, the frameworks of ribbed domes can have single chord or dou- ble chord ribs. Geometric system of the framework of a large-span metal dome governs the method of its erection which in its turn defines the structural solutions for the elements of the framework and the sequence of their assembly. The paper describes the following methods of erection of large-span domes: erection by crane from the ground with temporary supports, placement of the complete structure or large elements of the dome, and cantilever erection. The examples of large-span metal domes built in different countries of the world are reviewed with respect to the method of construction used. General characteristics of the structural system of the framework of each dome are presented. The examples are used to demonstrate that the method of construction of a large-span metal dome roof is dependent on the geometric system of its framework. It is noted that metal domes are widely used as structural solutions for roofs of buildings of different types. It is noted that erection with temporary supports of different types, or ground assembly are mostly used for the construction of relatively low double layer domes, or high single-layer domes. For large-span double-layer metal domes of considerable high the method of cantilever erection is usually preferred.

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(1):4-16

## Analysis of thin elastic shells

### NONLINEAR STABILITY OF SINUSOIDAL VELAROIDAL SHELL

#### Abstract

The nonlinear analysis of thin-walled shells is not a rarity, particularly the nonlinear strength one. Many works are devoted to linear and nonlinear analyses of shells of classical form: cylindrical, spherical, hemispherical, shallow, conical. The concept of shells of complex geometry appears when the coefficients of the first and second quadratic forms of their middle surfaces are functions of the curvilinear coordinates. Concerning nonlinearity, it is generally accepted that four different sources of nonlinearity exist in solid mechanics: the geometric nonlinearity, the material nonlinearity and the kinetic nonlinearity. The above theoretical aspect of the nonlinearity, applied to a sinusoidal velaroidal shell with the inner radius r0=1m, the outer radius R=20m and the number of waves n= 8, will give rise to the investigation of its nonlinear buckling resistance. The building material is a concrete. The investigation emphasizes more on the material and the geometric nonlinearities, which are more closed to the reality. Finite element model of the shell consists of 6400 elements and 3280 nodes, the total number of nodal unknown - 18991. For surface modelling was used flat shell elements with six degrees of freedom in the node. The boundary conditions cor- respond to hinged bearing on the outer and inner contours. The result of the investigation is the buckling force of the shell under self-weight and uniformly vertically distributed load on its area, the corresponding numerical values of displacements and the buckling mode

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(1):17-22

## Theory of elasticity

### STRESS-STRAIN STATE OF THE RECTANGULAR PLATES ON THE BASIS OF REFINED THEORY

#### Abstract

Two variants of a refined theory for calculation of the rectangular orthotropic plates stress-strain state are represented. The plate's state equations are presented in the form three-dimensional equations of elasticity theory. The components of the plate's stress-strain state are received as the polynomial func- tions on the coordinate which is normal to the middle plane. These functions are one or two degree higher than in the Kirchhoff-Love theory are used. The virtual displacements principle is applied to obtain the two-dimensional equations and its natural boundary conditions. The modified boundary conditions for standard cases of the plate mounting are formulated. Calculation of plate stress-strain is carried out by using Laplace transform, and then the number of arbitrary constants in the integration of differential equations systems thus is twice reduced. One of the refined theory distinctive features consist in direct integration of the three dimensional elasticity problems equilibrium equations at transverse normal and tangential stresses determination. As an example, the paper considers the calculation of a rectangular isotropic plate's stress-strain under a local load. The results obtained by the refined theories and by the classical theory are compared. The essential contribution of normal transverse stress of type "boundary layer" to the general stress- strain state of a plate is shown. The received results can be used in calculations and at tests for strength and durability of aviation and space-rocket and also engineering structures of different destination

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(1):23-32

### THE PROBLEM ON THE DYNAMICS OF A HOLLOW PRISM OF A RECTANGULAR CROSS SECTION

#### Abstract

In the article, the process of propagation of non-stationary waves in hollow rectangular semi-infinite prisms is studied for the first time. It is believed that in all 8 sides there are mixed boundary conditions, and impact is made on the end face of this prism. In the papers (1-3), using the integral transformations and replacing the sought values (three displacement components) through new successfully chosen functions (wave potentials), the system of three-dimensional Lame equations is reduced to the system of Bessel equations. On the other hand, it is well known that the selected mixed conditions on the surface of the body allow us to separate the values of different waves (longitudinal and transverse) on the same surface, i.e. all these waves propagate independently of each other. These two circumstances make it possible to obtain a new boundary value problem for each potential- function, separately. Solutions of these boundary-value problems for a whole prism are obtained, and for the selected boundary conditions of this article (sliding contact conditions). A kind of method was used that made it possible to generalize the resulting solution for the entire prism in the case of a hollow prism.

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(1):33-37

### RESOLVING EQUATIONS OF PLANAR DEFORMATION IN CYLINDRICAL COORDINATES FOR PHYSICALLY NONLINEAR CONTINUUM

#### Abstract

For planar deformations of continuum, which mechanical behavior is described by mathematical models, where physical relations have the form of cross dependence derivatives between the first invariant of the tensor and the second invariant of the voltage and stress deviator, the development of resolving equations in displacements in cylindrical coordinates is being analyzed. Two models are analyzed as examples: deformation theory of loose medium plasticity and deformation theory of concrete plasticity. The resolving equations system is a system of two quasilinear differential equations of second order at quotient derivatives from two independent variables - the displacement of continuum points at radial and tangential directions. Iteration methods are suggested for its integration. It is recommended to take the discussed question solution for physical linear continuum as initial solution approximation. Received equations can be used at evaluation of stress-strain state of physically nonlinear massive bodies with complex geometry.

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(1):38-45

## Analysis and design of building structures

### TRANSFORMATION ELEMENT BETWEEN THE DEPENDENCE OF THE FRAC- TURE MECHANICS AND THE EQUATIONS OF THE REINFORCED CONCRETE THEORY IN THE CONDITIONS OF A COMPLEX RESISTANCE

#### Abstract

The hypothesis of fracture mechanics is developed in the article and a universal short dual-console element is designed for reinforced concrete structures of buildings and structures. The proposed dual-console element is applicable to the evaluation of reinforced concrete structures resistance under conditions of various force and deformation effects, including torsion with bending. Simplified dependences are constructed for the energy functional and the specifics and features of the construction of a dual-console fracture mechanics element in the zones adjacent to the spatial cracks are considered taking into account the discontinuity effect. The dual-console element is the connecting link and serves as a transformational element between the dependencies of fracture mechanics and the equations of reinforced concrete theory.

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(1):46-56

### STRESS STATE OF A CANTILEVER CABLE HOLDER OF THE TYPE CCH-3; 4; 6

#### Abstract

Experimental studies of the loading of cable holders (console) type CCH, used as sup- ports for laying cables in passing wells, showed their excessively large dimensions (the thick- ness of the rib and bed), which leads to unnecessary material costs in the manufacture and, as a result, overestimation. Using the finite element analysis method in the software package Siemens NX via the NX NASTRAN solver, the intense state of cable holders (consoles) of the type CCH-3; 4; 6. As a geometric model, we used the solid solid model prepared in the Auto- Desk Inventor package. The possibility of reducing the size of the console, while maintaining load capacity, which can significantly reduce their materialoemkost without changing the strength parameters. The possible reduction in weight is approximately 22 ... 24% of the original value. Con- sidering that currently laid cables have a significantly lower mass, it is necessary to develop new GOSTs for the type of products to be considered. On the basis of the results obtained, it is also advisable to consider transition issues in the manufacture of consoles for new materials (plastics, composites, etc.) in order to increase their operational properties, further reducing the mass and possibly reducing costs

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(1):57-63

### INFLUENCE OF CONSTRUCTION OF TRANSPARENT COVERING ON EFFICIENCY OF CONCRETE HEAT TREATMENT IN SHUTTERING FORMS WITH USING SOLAR ENERGY

#### Abstract

The shuttering forms, equipped by inventory frames with transparent cover, are the simple solar energy equipment for heat treatment of reinforced concrete elements during their manufacturing at the plants. They are similar with solar collectors by their design and thermal-physical processes, taking place in them, with difference that the heat sink is hardening concrete. The research results of influence of transparent cover construction on efficiency of concrete heat treatment in shuttering forms with employment of solar energy in different climatic conditions are given in the article. The volume of energy, consumed and lost by concrete during its direct heating by solar energy in the simple solar energy equipment like solar collector, depends on the transparent cover construction. Under other same conditions, the increase of cover layers affects its transparency, which is characterized by the solar energy transmittance, but in this case, it reduces heat losses in environment, which are characterized by the coefficient of heat losses through transparent cover. One-layer and two-layer transparent covers are chosen for assessment of efficiency of heat treatment of concrete elements, because the increase of cover layers more than two reduces intensity of the heat sink warming in the daytime and it is accepted by scientists in solar energy field as pointless. Optimal number of transparent material layers in cover construction is determined based on energy assessment in result of thermal- physical calculation and experimental research. The economic losses for production of transparent cover due to the increase of its layers are taken into account in addition with energy assessment

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(1):64-69

## Seismic resistence

### FEASIBLITY EVALUATION FOR A PREDEFINED SEISMIC RESISTANCE OF STRUCTURES

#### Abstract

Nowadays seismic resistant structural design is based on force analysis and on representing the earthquake effect as equivalent static forces set as elastic response spectra (response spectrum method). These response spectra link the law of earth motion to the absolute acceleration of the structure's model. This approach takes no account of either the effect of intense motion duration or of the plastic behavior of the structure. The frequency content and the duration of earth oscillations immediately influence the energy taken in by the building and causing damage to its elements. In theoretical terms, the input energy depends on the model of the structure in question. The input energy is determined by a dynamic calculation for the selected model or by theoretical assessment. Then, the energy is compared to the energy capacity, i.e. maximum energy which can be conveyed to the building before it collapses. Conventionally, the energy capacity is compared to the plastic component of the input energy (absorbed by the building). This forms the basis for the energy method of seismic structural design. The present paper considers a seismic resistance feasibility calculation technique employing non-linear statistical analysis based on the energy-centered approach. Non-linear static and non-linear dynamic calculations were run for a three-story frame. The two methods were benchmarked against each other, the importance of the higher modes of vibration was exposed, the importance of analyzing their influence on the system's response was emphasized

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(1):70-79

## In memory of the friend

### Pamyati tovarishcha

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(1):80-80