# Vol 14, No 2 (2018)

**Year:**2018**Articles:**9**URL:**https://journals.rudn.ru/structural-mechanics/issue/view/1076**DOI:**https://doi.org/10.22363/1815-5235-2018-14-2

## Full Issue

## Analysis and design of building structures

### Finding the extreme values of operating characteristics for quality control of construction products

#### Abstract

The matter of control planning by variables is essentially the inverse problem of interval estimation. Therefore, when determining control plans (“n” is the sample size, “k” is the eligibility criterion), the results of interval estimation are used. The algorithm of interval estimation, proposed by L.N. Bolshev and E.A. Loginov, presupposes finding the upper and lower bounds of the operational characteristic of quality control, which in turn represents the probability of acceptance of the batch with a quality level not exceeding the consumer risk. In this case, the probability of batch rejection is not more than the manufacturer risk. In this article, an attempt is made to find the extreme values of the operating characteristic in an explicit form. As a result, operative characteristics formulas were obtained in an explicit form, which made it possible to significantly simplify the determination of control plans with bilateral tolerance for the controlled parameter that characterizes a specific product. In construction industry, any sign on which the reliability of the construction product is characterized is implied as a controlled parameter.

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(2):84-91

### Superposition principle as the fundamental error of the creep theory and standards of the reinforced concrete

#### Abstract

The errors in the foundations of the modern theory of creep of reinforced concrete caused by the use of the principle of superposition, which is an expansive interpretation of the principle (scheme) of the linear superposition of Boltzmann, are revealed and investigated. Extensive interpretation arises from the following circumstances: the phenomenon of aging of concrete; changes in the short-term properties of concrete with age τ at the time of its loading; nonlinearity of creep deformation, starting from the lowest loading levels; the use of “chain models” in the form of a series connection of several bodies, for example - the theory of Maslov, the theory of aging, a viscous element; addition of short-term properties of concrete to the properties of its creep; expanding interpretation of the compliance function for difference kernels. In the international norms of creep of reinforced concrete only linear creep of concrete and instantaneous linear properties are taken into account; their authors call their developments “a new advanced format developed in recent decades by international standards institutions”. However, these format estimates are erroneous. According to the Eurocode, a short-term diagram of concrete σ-ε has a descending section and a limited extent; and the floor-duchit of concrete is nonlinear. The founders of the theory are A.A. Gvozdev, N.Kh. Harutyunyan, S.V. Aleksandrovsky, P.I. Vasilyev - repeatedly indicate: “creep-concrete deformations are non-linearly dependent on stresses, starting from the lowest levels”. The results of the analysis published by the authors in the journal of Structural Mechanics of Engineering Constructions and Buildings No. 6 of 2017 and No. 3 of 2016 are supplemented. The article was written in accordance with the recommendations of the round table held in the RUDN University on June 9, 2016, under the direction of the D.Sc., prof. S.N. Krivoshapko.

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(2):92-104

### Analytical calculation of the deflection of a beam truss with double bracing

#### Abstract

A statically determinate planar truss has rectilinear belts and a triangular lattice consisting of double braces. The four links make it seemingly statically indeterminate. The derivation of the formula for the dependence of the deflection on its dimensions and the number of panels is given. Forces in rods are determined in symbolic form by cutting out nodes from the solution of a system of linear equations in the system of computer mathematics Maple. To determine the deflection, the Maxwell - Mohr’s formula is used. Rods (except all rigid support) are assumed to be elastic with the same rigidity. The generalization of individual solutions to an arbitrary number of panels is done by induction. Operators of the Maple system from the calculation data yield linear homogeneous recurrence equations for the coefficients of the desired formula. The solutions of these equations give the general terms of the obtained sequences. Formulas for three types of loads are obtained and compared (the uniform loading of the nodes of the lower and upper belts and the concentrated force in the middle of the span). Curves of the dependence of deflection on the number of panels have weakly expressed minima. The dependencies of the forces in the most compressed and stretched rods on the number of panels are derived. Also given are asymptotic estimates for solutions in accordance with the number of panels in fixed spans of the construction and at a given total load.

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(2):105-111

## Analysis and design of machine-building structures

### Analysis of pressure stabilizer elliptic chambers on the deformed state by numerical method

#### Abstract

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(2):112-119

## Numerical methods of structures’ analysis

### The analysis of reinforced concrete slabs strengthened by composite fabrics by the finite element method

#### Abstract

The finite element method of calculation of reinforced concrete slabs strengthened with composite fabrics based on carbon fibers, implemented in the PRINS program, is considered. The method is designed for analyzing the stress-strain state of reinforced concrete structures when cracks in concrete and plastic deformations in the reinforcement arise. The calculation is carried out in increments, and at each stage of loading a variable stiffness matrix is used. Its constant part represents the stiffness matrix at the beginning of the loading stage, and the variable one is calculated taking into account the stress-strain state at the end of the current iteration. The variable part of the stiffness matrix, multiplied by the displacement vector found at the previous iteration, is transferred to the right side of the equation system and is considered to be an additional load. When cracks occur or when plastic strains appear, the stresses are corrected in accordance with the specified deformation diagrams. Therefore, at the end of the loading step the equilibrium conditions are checked. If necessary, the external and internal forces are balanced. When considering plastic deformations in concrete and reinforcement, the theory of plastic flow and the Huber - Mises yield criterion, modified taking into account the experimental studies of Kupfer et al., are used. An example of the reinforced concrete slab analysis with different variants of strengthening by composite and without strengthening is given. The results of the calculation are analyzed. The possibility of studying the stress-strain state throughout the entire path of loading of reinforced concrete slabs up to destruction is shown.

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(2):120-131

## Buckling analysis

### The dynamic stability of physically nonlinear plate systems under biaxial compression

#### Abstract

The article presents the method of dynamic stability analysis of plate systems with nonshifting ribs. A plate system under the biaxial dynamic compression loads is considered. The Kirchhoff - Love hypotheses, the nonlinear-elastic body hypothesis are considered the basis of the calculations. The material of the plate system is assumed to be physically nonlinear, stress-deformation diagram is approximated in the form of a cubic polynomial. The displacement of points in normal direction to middle plane of plates is presented in the form of Vlasov expansion. To derive the basic differential equations of stability, the strainenergy method and Vlasov's variation method are used. The extreme value of total energy of the system is defined using Euler - Lagrange equation, after solving of which the set of basic nonlinear differential equations of buckling of the plate system with non-shifting ribs under dynamic compression loads is given. As an example, the stability calculation of physically nonlinear T-shaped plate system hinge-supported along the contour is carried out. Buckling of the plate system occurs longitudinally on one half-wave of sinusoid. At the solution of a task in the first approximation, a nonlinear differential equation is derived, the numerical integration of which was carried out by the Runge - Kutta method. Based on the results of the calculations, graphs of the relative magnitude of deflection against the dynamic coefficient are plotted. The influence of the degree of physical nonlinearity of the material, the rate of change of the dynamic compressive load on the dynamic criterion of buckling of the plate system was studied.

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(2):132-141

## Mechanics of liquids

### The pairing of a swirling spillway to the lower pool through the thrown jets

#### Abstract

In the modern practice of hydraulic engineering pressure hydrosystems reach H ≥ 200 m. In these conditions the most efficient spillway structure is the vortex shaft spillway. In this paper, the authors consider the conjugation of the swirled flow at the outlet of the discharge conduit with downstreem by thrown jet with a residual twist. In the scheme with jet drop, the residual twist of the flow during the release from the vortex spillway contributes to the expansion of the jet in the air, reducing the specific flow rate, as well as reducing the dynamic loads on the lower bed. The comparison with the jet thrown from the sock of the drainage dam at the same speed parameters (i.e. at the speed of 20-25 m/s on the lip) is carried out. The formula obtained is simple enough to determine the planned outline of the discarded jet. The scheme of conjugation of the jet with the surface of the lower tail water, as well as the calculation scheme to determine the specific discharge of the downward swirling jet.

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(2):142-153

## Geometrical investigations of middle surfaces of shells

### Constrained Construction of Planar Delaunay Triangulations without Flipping

#### Abstract

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(2):154-174

## In memory of the friend

### Vitalii Mikhailovich Bondarenko (22.06.1925 - 22.02.2018)

**Structural Mechanics of Engineering Constructions and Buildings**. 2018;14(2):175-176