"Вестник МГСУ"

Differential equations of motion for a bar are provided in this paper. The bar is exposed to the applied force that intensifies as the time progresses. The condition substantiating the trans-versal inertia force is identified using the equations. On top of the emerging inertia force, brief high-speed stress increases the yield stress of the material.The external force is accompanied by the eccentricity. Therefore, linear dimensions of the bar and its eccentricity make plastic behaviour possible both in compressed and stretched areas of the rod sections. Patterns of distribution of plastic deformations (one-sided and double-sided yield) are generated using the equations of motion for each case. Cauchy problems are supple- mented by the incoming conditions according to the principle of continuity of displacement and velocity.The criterion of stability loss is a condition when the variation of the exterior torque equals to the variation of the interior torque. At the same time, the variation of a longitudinal force must be equal to zero. Having completed a series of transformations, the author obtains the stability loss functional. It is calculated simultaneously with the motion equation. When the functional is equal to zero, the bearing capacity is exhausted.Moreover, there is a simplified method of identifying the critical force. The comparison of values with the testing findings demonstrates the efficiency of employment of the approximate method.

Installation of antenna masts and towers that have cellular signal transmission equipment
mounted represents a relevant problem in the urban development. Given its density, as well as the
multiplicity of multistory residential and offi ce buildings, masts can be mounted onto existing buildings
and structures. For this purpose, the analysis of a metal mast itself and a ceiling panel on which it is
to rest should be performed in respect of different types of loading. This task is of utmost importance,
since original designs of buildings fail to take account of any supplementary static or dynamic loads.
Numerical and analytical methods are used for the purpose of the analysis. The analysis of cellular
signal transmission masts is performed numerically with the help of a software programme, while the
calculation of the ceiling panel is performed on the basis of a combined scheme. As a result, the authors
demonstrate the safety of installation of high-altitude masts onto existing structures exposed to
varying loads, including wind and ice loads.

Concrete arches are widely used in the construction of underground facilities. The analysis of their work under dynamic loads (blasting, shock, seismic) will improve the efficiency of design and application. The article addresses the problems of calculation of reinforced concrete arches in the ground in terms of the action of dynamic load - compression wave. The calculation is made basing on the decision of a closed system of equations that allows performing the calculation of elastic-plastic curved concrete structures under dynamic loads. Keeping in mind the properties of elastic-plastic reinforcement and concrete in the process of design variations, σ-ε diagrams are variable. The calculation is performed by the direct solution of differential equations in partial derivatives. The result is based on a system of ordinary differential equations of the second order (expressing the transverse and longitudinal oscillations of the structure) and the system of algebraic equations (continuity condition of deformation). The computer program calculated three-hinged reinforced concrete arches. The structural calculations were produced by selection of the load based on the criteria of reaching the first limit state: ultimate strain of compressed concrete; ultimate strain tensile reinforcement; the ultimate deformation of the structure. The authors defined all the characteristics of the stress-strain state of the structure. The presented graphs show the change of bending moment and shear force in time for the most loaded section of the arch, the dependence of stresses and strains in concrete and reinforcement, stress changes in time for the cross-sectional height. The peculiarity of the problem is that the action of the load provokes the related dynamic forces - bending moment and longitudinal force. The calculations allowed estimating the carrying capacity of the structure using the criteria of settlement limit states. The decisive criterion was the compressive strength of concrete.

The physical reasons for building structures destruction are both the forces arising at stress-strain state of construction elements and external influences arising at emergency situations, as well as their moments, impulses and periodic impulses with the frequencies close to of fluctuations frequencies of construction elements. We shall call the mathematical calculation models for the parameters-reasons of destructions the basic models. The basic models of destruction of building structures elements allow not only providing necessary level of reliability and survivability of the elements and the construction as a whole already at the stage of their design, but also giving the chance, at their corresponding completion, to provide rational decisions on the general need of recovery works and their volume depending on destruction level. Especially important for rational design decisions development, which ensure the demanded constructional safety of building structures, is library creation of the basic mathematical models of standard processes of bearing elements destructions for standard construction designs for the purpose of the further forecast (assessment) of the level and probabilities of standard destructions. Some basic mathematical models of destructions processes of the standard elements of building structures are presented in the present article. A model of accounting for construction defects and a model of obtaining requirements to probabilities of partial destructions of a construction are given. Both of these models are probabilistic.

Subject: a computational scheme of the bottom of deep foundation for analyzing vibrations of the “pile-heavy foundation” system is proposed. It is shown that, in this case, accounting for inertial forces of the pile and friction along the lateral surface of the pile leads to a non-periodic (non-harmonic) damped oscillation of the deep foundation. Research objectives: assessment of displacement and resistance along the lateral surface of a pre-fabricated reinforced concrete pile under vibratory immersion; estimation of key factors affecting resistance of the pile in vibratory immersion. Materials and methods: when solving the problem of interaction between the pile and the surrounding soil during vibratory immersion, analytical solutions of the static and dynamic problems using modified rheological models of soils were used. Analytical solutions are obtained using the software package MathCAD. Comparison of the results of analytical calculations with numerical solutions is performed in the PLAXIS 2D geotechnical software package that implements the finite element method. In the numerical solution of the problem of interaction between the pile and the surrounding soil, an elastoplastic model with Mohr-Coulomb hardening was used. Results: when solving the problem of oscillation of the “system”, various contact models are considered for calculations, including elastic, nonlinear and rheological, taking into account time-dependent hardening. Rheological parameters of soils are used, which can be determined on the basis of special laboratory studies. Conclusions: the proposed scheme for interaction between the pile and the surrounding soil during vibratory immersion describes, with sufficient accuracy, the oscillations of a weighty pile on a viscoelastic soil base, taking into account the resistance along the lateral surface and the frictional forces at the pile-soil contact. The performed analytical and numerical analysis of the proposed model showed qualitative agreement. Allowance for friction along the lateral surface of a weighty pile significantly influences the vibration characteristics of a deep foundation.